Edit Profile (opens in new tab) Lieb, Elliott Hershel Compute Distance To: Compute Author ID: lieb.elliott-h Published as: Lieb, Elliott H.; Lieb, E. H.; Lieb, Elliot H.; Lieb, Elliott; Lieb, Eliott H.; Lieb, E. more...less Homepage: https://web.math.princeton.edu/~lieb/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef Awards: Carl Friedrich Gauss Prize (2022) Documents Indexed: 257 Publications since 1957, including 11 Books 1 Contribution as Editor · 2 Further Contributions Biographic References: 10 Publications Co-Authors: 80 Co-Authors with 201 Joint Publications 2,609 Co-Co-Authors all top 5 Co-Authors 56 single-authored 37 Seiringer, Robert 32 Frank, Rupert L. 29 Yngvason, Jakob 26 Carlen, Eric Anders 24 Loss, Michael 23 Solovej, Jan Philip 12 Almgren, Frederick Justin jun. 7 Brézis, Haïm 7 Siedentop, Heinz Karl Heinrich 6 Brascamp, Herm Jan 5 Jauslin, Ian 5 Thomas, Lawrence E. 4 Giuliani, Alessandro 4 Lebowitz, Joel Louis 4 Lewin, Mathieu 3 Aizenman, Michael 3 Bach, Volker 3 Heilmann, Ole J. 3 Mattis, Daniel Charles 3 Nachtergaele, Bruno 3 Simon, Barry 3 Yau, Horng-Tzer 2 Benguria, Rafael D. 2 Coron, Jean-Michel 2 Daubechies, Ingrid Chantal 2 Liniger, Werner 2 McCann, Robert J. 2 Rougerie, Nicolas 2 Wightman, Arthur Strong 1 Almgren, Robert F. 1 Ball, Keith Martin 1 Barnes, John F. 1 Bellazzini, Jacopo 1 Beyer, William A. 1 Browder, William 1 Caffarelli, Luis Ángel 1 Chayes, Jennifer Tour 1 Chayes, Lincoln 1 Conlon, Joseph G. 1 Cordero-Erausquin, Dario 1 Davies, Edward Brian 1 Decker, Colin 1 DeWitt-Morette, Cécile 1 Epstein, David Bernard Alper 1 Epstein, Henri 1 Fellbaum, Christiane 1 Flato, Moshé 1 Freericks, James K. 1 Fröhlich, Jürg Martin 1 Ginibre, Jean 1 Glaser, Vladimir Jurko 1 Glimm, James G. 1 Griesemer, Marcel 1 Griffiths, Robert B. 1 Hepp, Klaus 1 Hundertmark, Dirk 1 Iantchenko, Alexei 1 Ivanisvili, Paata 1 Jaffe, Arthur Michael 1 Jansen, Sabine 1 Jerison, David S. 1 Kennedy, Tom 1 Kleitman, Daniel J. 1 Koppe, Heinz 1 Kulkarni, Sanjeev R. 1 Kusner, Robert B. 1 Lanford, Oscar E. III 1 Laptev, Ari 1 Lazarev, Oleg 1 Lewis, Roger T. 1 Luttinger, Joaquin M. 1 Marden, Albert 1 Morgan, Frank 1 Narnhofer, Heide 1 Osherson, Daniel N. 1 Ostrover, Yaron 1 Pedersen, Gert Kjærgård 1 Poor, Harold Vincent 1 Predd, Joel B. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Reuvers, Robin 1 Ruelle, David Pierre 1 Ruskai, Mary Beth 1 Sabin, Julien 1 Sakakura, A. Y. 1 Sanches Fernandes, K. 1 Schultz, Theodore 1 Seiler, Ruedi 1 Sherman, Seymour 1 Stein, Elias Menachem 1 Stephens, Benjamin K. 1 Stora, Raymond 1 Sullivan, John M. jun. 1 Taylor, Jean Ellen 1 Temperley, H. V. N. 1 Thirring, Walter E. 1 Travaglia, Marcos Vinicio 1 Ueltschi, Daniel 1 Yamazaki, Kazuo 1 Yang, Yisong all top 5 Serials 44 Communications in Mathematical Physics 11 Journal of Mathematical Physics 11 Journal of Statistical Physics 8 Letters in Mathematical Physics 8 Advances in Mathematics 7 Physical Review, II. Series 4 Inventiones Mathematicae 4 Journal of Functional Analysis 4 Annals of Mathematics. Second Series 3 Physica A 3 Reviews in Mathematical Physics 3 Bulletin of the American Mathematical Society. New Series 3 Physical Review Letters 2 Reviews of Modern Physics 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Studies in Applied Mathematics 2 Journal of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Linear Algebra and its Applications 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 SIAM Journal on Mathematical Analysis 2 Notices of the American Mathematical Society 2 Advances in Theoretical and Mathematical Physics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Bulletin of the American Mathematical Society 2 Journal of Combinatorial Theory 2 Graduate Studies in Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Pure and Applied Analysis 1 International Journal of Modern Physics B 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 Helvetica Physica Acta 1 IEEE Transactions on Information Theory 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Physics Reports 1 Reports on Mathematical Physics 1 Arkiv för Matematik 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Publications Mathématiques 1 Journal of Economic Theory 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Advances in Applied Mathematics 1 IMRN. International Mathematics Research Notices 1 Annals of Physics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Experimental Mathematics 1 Calculus of Variations and Partial Differential Equations 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Mathematical Research Letters 1 Methods and Applications of Analysis 1 Documenta Mathematica 1 ELA. The Electronic Journal of Linear Algebra 1 Journal of the European Mathematical Society (JEMS) 1 Annales Henri Poincaré 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Mathematics and Mechanics 1 Oberwolfach Seminars 1 Physical Review A, Third Series 1 Bulletin of Mathematical Sciences 1 Journal de l’École Polytechnique – Mathématiques 1 Princeton Series in Physics all top 5 Fields 108 Quantum theory (81-XX) 79 Statistical mechanics, structure of matter (82-XX) 53 Partial differential equations (35-XX) 42 Functional analysis (46-XX) 24 Operator theory (47-XX) 23 Real functions (26-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Information and communication theory, circuits (94-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 14 Probability theory and stochastic processes (60-XX) 13 History and biography (01-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Measure and integration (28-XX) 9 Classical thermodynamics, heat transfer (80-XX) 6 Combinatorics (05-XX) 5 General and overarching topics; collections (00-XX) 5 Potential theory (31-XX) 5 Astronomy and astrophysics (85-XX) 4 Difference and functional equations (39-XX) 3 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 220 Publications have been cited 9,874 times in 7,103 Documents Cited by ▼ Year ▼ A relation between pointwise convergence of functions and convergence of functionals. Zbl 0526.46037Brézis, Haïm; Lieb, Elliott H. 1,070 1983 Analysis. 2nd ed. Zbl 0966.26002Lieb, Elliott H.; Loss, Michael 790 2001 Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Zbl 0527.42011Lieb, Elliott H. 575 1983 Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Zbl 0369.35022Lieb, Elliott H. 447 1977 On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. Zbl 0334.26009Brascamp, Herm Jan; Lieb, Elliott H. 368 1976 Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ’percolation’ problem. Zbl 0211.56703Temperley, H. V. N.; Lieb, Elliott H. 263 1971 Two soluble models of an antiferromagnetic chain. Zbl 0129.46401Lieb, Elliott H.; Schultz, Theodore; Mattis, D. 249 1961 Theory of monomer-dimer systems. Zbl 0228.05131Heilmann, Ole J.; Lieb, Elliott H. 220 1972 Exact analysis of an interaction Bose gas. I: The general solution and the ground state. Zbl 0138.23001Lieb, Elliott H.; Liniger, Werner 212 1963 Harmonic maps with defects. Zbl 0608.58016Brézis, Haïm; Coron, Jean-Michel; Lieb, Elliott H. 193 1986 Convex trace functions and the Wigner-Yanase-Dyson conjecture. Zbl 0267.46055Lieb, Elliott H. 191 1973 The mathematics of the Bose gas and its condensation. Zbl 1104.82012Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 187 2005 The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568Lieb, Elliott H.; Simon, Barry 180 1977 The Chandrasekhar theory of stellar collapse as the limit quantum mechanics. Zbl 0641.35065Lieb, Elliott H.; Yau, Horng-Tzer 163 1987 Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Zbl 0339.26020Brascamp, Herm Jan; Lieb, Elliott H. 142 1976 The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Zbl 0478.49035Benguria, Rafael; Brézis, Haïm; Lieb, Elliott H. 138 1981 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 137 2008 Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Zbl 0342.35044Lieb, Elliott H.; Thirring, Walter E. 136 1976 Sharp uniform convexity and smoothness inequalities for trace norms. Zbl 0803.47037Ball, Keith; Carlen, Eric A.; Lieb, Elliott H. 135 1994 A general rearrangement inequality for multiple integrals. Zbl 0286.26005Brascamp, H. J.; Lieb, Elliott H.; Luttinger, J. M. 127 1974 Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014Almgren, Frederick J. jun.; Lieb, Elliott H. 111 1989 On the lowest eigenvalue of the Laplacian for the intersection of two domains. Zbl 0538.35058Lieb, Elliott H. 106 1983 Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael 104 2001 Bounds on the eigenvalues of the Laplace and Schrödinger operators. Zbl 0329.35018Lieb, Elliott H. 101 1976 The classical limit of quantum spin systems. Zbl 1125.82305Lieb, Elliott H. 99 1973 Gaussian kernels have only Gaussian maximizers. Zbl 0726.42005Lieb, Elliott H. 90 1990 Thomas-Fermi and related theories of atoms and molecules. Zbl 1114.81336Lieb, Elliott H. 90 1981 The stability of matter in quantum mechanics. Zbl 1179.81004Lieb, Elliott H.; Seiringer, Robert 89 2009 Minimum action solutions of some vector field equations. Zbl 0579.35025Brézis, Haïm; Lieb, Elliott H. 86 1984 The stability and instability of relativistic matter. Zbl 0686.35099Lieb, Elliott H.; Yau, Horng-Tzer 81 1988 Thomas-Fermi and related theories of atoms and molecules. Zbl 1049.81679Lieb, Elliott H. 76 1981 Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip 75 1994 Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004Lieb, Elliott H.; Seiringer, Robert 72 2006 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 72 2012 A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 72 2001 Sobolev inequalities with remainder terms. Zbl 0577.46031Brézis, Haïm; Lieb, Elliott H. 68 1985 Stability of Coulomb systems with magnetic fields. I: The one-electron atom. Zbl 0595.35098Fröhlich, Jürg; Lieb, Elliott H.; Loss, Michael 67 1986 Proof of an entropy conjecture of Wehrl. Zbl 0385.60089Lieb, Elliott H. 65 1978 Exact analysis of an interacting Bose gas. II: The excitation spectrum. Zbl 0138.23002Lieb, Elliott H. 65 1963 Analysis. Zbl 0873.26002Lieb, Elliott H.; Loss, Michael 62 1996 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 57 2013 The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei. Zbl 1049.82501Lieb, Eliott H.; Lebowitz, Joel L. 56 1972 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 51 2010 Integral bounds for radar ambiguity functions and Wigner distributions. Zbl 0704.46050Lieb, Elliott H. 49 1990 A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002Carlen, E. A.; Lieb, E. H.; Loss, M. 47 2004 Some operator inequalities of the Schwarz type. Zbl 0274.46045Lieb, Elliott H.; Ruskai, Mary Beth 45 1974 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 44 2006 The physics and mathematics of the second law of thermodynamics. Zbl 1027.80504Lieb, Elliott H.; Yngvason, Jakob 41 1999 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 41 1996 The stability of matter: From atoms to stars. Zbl 0698.35135Lieb, Elliott H. 40 1990 Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions. Zbl 0807.47058Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob 39 1994 Exact ground state energy of the strong-coupling polaron. Zbl 0874.60095Lieb, Elliott H.; Thomas, Lawrence E. 38 1997 On characteristic exponents in turbulence. Zbl 0598.76054Lieb, Elliott H. 37 1984 Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma. Zbl 0348.26011Brascamp, H. J.; Lieb, Elliott H. 37 1975 Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080Lieb, Elliott H.; Loss, Michael 36 2003 Proofs of some conjectures on permanents. Zbl 0144.26802Lieb, Elliott H. 36 1966 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 36 2012 A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Zbl 0929.34076Hundertmark, Dirk; Lieb, Elliott H.; Thomas, Lawrence E. 35 1998 Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities. Zbl 0796.46054Carlen, Eric A.; Lieb, Elliott H. 35 1993 The ground state energy of a dilute two-dimensional Bose gas. Zbl 1115.82306Lieb, Elliott H.; Yngvason, Jakob 34 2001 Some convexity and subadditivity properties of entropy. Zbl 0308.94020Lieb, Elliott H. 33 1975 Ground state energy of the one-component charged Bose gas. Zbl 1042.82004Lieb, Elliott H.; Solovej, Jan Philip 33 2002 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015Carlen, Eric A.; Lieb, Elliott H. 33 2008 Ordering energy levels of interacting spin systems. Zbl 0101.45302Lieb, Elliott H.; Mattis, Daniel 32 1962 Concavity properties and a generating function for Stirling numbers. Zbl 0164.33002Lieb, Elliott H. 32 1968 Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013Almgren, Frederick J. jun.; Lieb, Elliot H. 31 1988 The ground state energy and density of interacting bosons in a trap. Zbl 1043.82515Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 31 2000 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 31 2015 Long range atomic potentials in Thomas-Fermi theory. Zbl 0416.35066Brézis, Haïm; Lieb, Elliott H. 30 1979 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303Lieb, Elliott H.; Solovej, Jan Philip 30 2004 One-electron relativistic molecules with Coulomb interaction. Zbl 0946.81522Daubechies, Ingrid; Lieb, Elliott H. 29 1983 Fluxes, Laplacians, and Kasteleyn’s theorem. Zbl 0787.05083Lieb, Elliott H.; Loss, Michael 29 1993 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107Lieb, Elliott H.; Seiringer, Robert 27 2003 Asymptotics of heavy atoms in high magnetic fields. I: Lowest Landau band regions. Zbl 0800.49041Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob 27 1994 Stability of matter in magnetic fields. Zbl 1020.81957Lieb, Elliott H.; Loss, Michael; Solovej, Jan Philip 24 1995 The thermodynamic limit for jellium. Zbl 0973.82500Lieb, Elliott H.; Narnhofer, Heide 24 1975 An itinerant electron model with crystalline or magnetic long range order. Zbl 1002.82508Kennedy, Tom; Lieb, Elliott H. 24 1986 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2014 Stability of Coulomb systems with magnetic fields. II. The many-electron atom and the one-electron molecule. Zbl 0607.35082Lieb, Elliott H.; Loss, Michael 23 1986 Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313Lieb, Elliott H.; Seiringer, Robert 23 2004 Co-area, liquid crystals, and minimal surfaces. Zbl 0645.58015Almgren, F.; Browder, W.; Lieb, E. H. 22 1988 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 21 2014 Studies in mathematical physics. Essays in honor of Valentine Bargmann. Zbl 0326.00007 20 1976 One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 19 2004 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 19 2013 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040Lieb, Elliott H.; Loss, Michael 18 2002 Ground-state energy and effective mass of the polaron. Zbl 0100.42504Lieb, Elliott H.; Yamazaki, Kazuo 18 1958 Theory of ferromagnetism and the ordering of electronic energy levels. Zbl 0118.46202Lieb, Elliott H.; Mattis, D. 18 1962 A guide to entropy and second law of thermodynamics. Zbl 1038.80504Lieb, Elliott H.; Yngvason, Jakob 15 1998 The number of bound states of one-body Schrödinger operators and the Weyl problem. Zbl 0445.58029Lieb, Elliott H. 15 1980 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 15 2009 An inequality of Hadamard type for permanents. Zbl 1116.15015Carlen, Eric; Lieb, Elliott H.; Loss, Michael 15 2006 A Minkowski type trace inequality and strong subadditivity of quantum entropy. Zbl 0933.47014Carlen, Eric A.; Lieb, Elliott H. 14 1999 Poincaré inequalities in punctured domains. Zbl 1048.26012Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 14 2003 Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216Lieb, Elliott H.; Yang, Yisong 14 2012 Symmetry of the Ginzburg-Landau minimizer in a disc. Zbl 0842.49014Lieb, Elliott H.; Loss, Michael 14 1994 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116Lieb, Elliott H.; Solovej, Jan Philip 14 2014 An \(L^ p\) bound for the Riesz and Bessel potentials of orthonormal functions. Zbl 0517.46025Lieb, Elliott H. 13 1983 Inequalities for some operator and matrix functions. Zbl 0324.15013Lieb, Elliott H. 13 1976 The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009Lieb, Elliott H.; Wu, F. Y. 13 2003 Analysis of a simple equation for the ground state of the Bose gas. II: Monotonicity, convexity, and condensate fraction. Zbl 1477.35189Carlen, Eric A.; Jauslin, Ian; Lieb, Elliott H. 1 2021 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020Frank, Rupert L.; Lieb, Elliott H. 1 2021 Wehrl-type coherent state entropy inequalities for \(\mathrm{SU}(1,1)\) and its \(AX+B\) subgroup. Zbl 1480.81064Lieb, Elliott H.; Solovej, Jan Philip 1 2021 The local density approximation in density functional theory. Zbl 1435.35320Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 9 2020 Divergence of the effective mass of a polaron in the strong coupling limit. Zbl 1446.81045Lieb, Elliott H.; Seiringer, Robert 4 2020 Analysis of a simple equation for the ground state energy of the Bose gas. Zbl 1465.35345Carlen, Eric A.; Jauslin, Ian; Lieb, Elliott H. 3 2020 Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 1479.46029Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 1 2020 Local incompressibility estimates for the Laughlin phase. Zbl 1410.82009Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob 5 2019 Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062Frank, Rupert L.; Lieb, Elliott H. 2 2019 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040Frank, Rupert; Lieb, Elliott H. 12 2018 Statistical mechanics of the uniform electron gas. (Mécanique statistique pour le gaz uniforme d’électrons.) Zbl 1404.82003Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 11 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 9 2018 Rigidity of the Laughlin liquid. Zbl 1398.81326Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob 6 2018 Nematic liquid crystal phase in a system of interacting dimers and monomers. Zbl 1400.82320Jauslin, Ian; Lieb, Elliott H. 2 2018 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091Frank, Rupert L.; Lieb, Elliott H. 7 2017 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 13 2016 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 11 2016 A Pfaffian formula for monomer-dimer partition functions. Zbl 1342.82161Giuliani, Alessandro; Jauslin, Ian; Lieb, Elliott H. 5 2016 On a quantum entropy power inequality of Audenaert, Datta, and Ozols. Zbl 1341.81015Carlen, Eric A.; Lieb, Elliott H.; Loss, Michael 3 2016 Entropy and entanglement bounds for reduced density matrices of fermionic states. Zbl 1342.81031Carlen, Eric A.; Lieb, Elliott H.; Reuvers, Robin 3 2016 Proof of the Wehrl-type entropy conjecture for symmetric \({SU(N)}\) coherent states. Zbl 1365.81030Lieb, Elliott H.; Solovej, Jan Philip 1 2016 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 31 2015 Columnar phase in quantum dimer models. Zbl 1320.82011Giuliani, Alessandro; Lieb, Elliott H. 2 2015 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2014 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 21 2014 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116Lieb, Elliott H.; Solovej, Jan Philip 14 2014 Remainder terms for some quantum entropy inequalities. Zbl 1292.81021Carlen, Eric A.; Lieb, Elliott H. 13 2014 Formation of stripes and slabs near the ferromagnetic transition. Zbl 1302.82018Giuliani, Alessandro; Lieb, Elliott H.; Seiringer, Robert 6 2014 Equivalence of two definitions of the effective mass of a polaron. Zbl 1295.81055Lieb, Elliott H.; Seiringer, Robert 5 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Entropy meters and the entropy of non-extensive systems. Zbl 1371.80005Lieb, Elliott H.; Yngvason, Jakob 4 2014 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 3 2014 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 57 2013 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 19 2013 Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures. Zbl 1270.26016Carlen, Eric A.; Cordero-Erausquin, Dario; Lieb, Elliott H. 7 2013 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 7 2013 The entropy concept for non-equilibrium states. Zbl 1371.80004Lieb, Elliott H.; Yngvason, Jakob 5 2013 On an extension problem for density matrices. Zbl 1282.81020Carlen, Eric A.; Lebowitz, Joel L.; Lieb, Elliott H. 3 2013 A smooth complex generalization of the Hobby-Rice theorem. Zbl 1295.41025Lazarev, Oleg; Lieb, Elliott H. 3 2013 Unique equilibria and substitution effects in a stochastic model of the marriage market. Zbl 1275.91098Decker, Colin; Lieb, Elliott H.; McCann, Robert J.; Stephens, Benjamin K. 3 2013 Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 2 2013 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 72 2012 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 36 2012 Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216Lieb, Elliott H.; Yang, Yisong 14 2012 Binding of polarons and atoms at threshold. Zbl 1250.82046Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Bounds for entanglement via an extension of strong subadditivity of entropy. Zbl 1254.81019Carlen, Eric A.; Lieb, Elliott H. 7 2012 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 4 2012 Further implications of the Bessis-Moussa-Villani conjecture. Zbl 1257.82009Lieb, Elliott H.; Seiringer, Robert 1 2012 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 13 2011 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013Frank, Rupert L.; Lieb, Elliott H. 5 2011 Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 2 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 51 2010 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 11 2010 Localization of multidimensional Wigner distributions. Zbl 1314.81129Lieb, Elliott H.; Ostrover, Yaron 4 2010 The stability of matter in quantum mechanics. Zbl 1179.81004Lieb, Elliott H.; Seiringer, Robert 89 2009 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 15 2009 Probabilistic coherence and proper scoring rules. Zbl 1367.94139Predd, Joel B.; Seiringer, Robert; Lieb, Elliott H.; Osherson, Daniel N.; Poor, H. Vincent; Kulkarni, Sanjeev R. 10 2009 Symmetry breaking in Laughlin’s state on a cylinder. Zbl 1155.81032Jansen, S.; Lieb, E. H.; Seiler, R. 5 2009 Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. Zbl 1190.15009Carlen, Eric A.; Lieb, Elliott H. 3 2009 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 137 2008 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015Carlen, Eric A.; Lieb, Elliott H. 33 2008 Brascamp–Lieb inequalities for non-commutative integration. Zbl 1173.46045Carlen, Eric A.; Lieb, Elliott H. 2 2008 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 12 2007 Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 5 2007 Bose-Einstein condensation and spontaneous symmetry breaking. Zbl 1160.82308Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 4 2007 Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004Lieb, Elliott H.; Seiringer, Robert 72 2006 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 44 2006 An inequality of Hadamard type for permanents. Zbl 1116.15015Carlen, Eric; Lieb, Elliott H.; Loss, Michael 15 2006 Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J. 12 2006 Ground-state energy of a dilute Fermi gas. Zbl 1114.82004Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip 3 2006 Some matrix rearrangement inequalities. Zbl 1197.15011Carlen, Eric; Lieb, Elliott H. 2 2006 Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V. 2 2006 The mathematics of the Bose gas and its condensation. Zbl 1104.82012Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 187 2005 The quantum-mechanical many-body problem: the Bose gas. Zbl 1113.82007Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 7 2005 Stronger subadditivity of entropy. Zbl 1227.82012Lieb, Elliott H.; Seiringer, Robert 5 2005 The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field. I: The lower bound. Zbl 1115.81064Lieb, Elliott H.; Loss, Michael 5 2005 One-dimensional behavior of dilute Bose gases in traps. Zbl 1106.82004Seiringer, Robert; Lieb, Elliott H.; Yngvason, Jakob 5 2005 The stability of matter: From atoms to stars. Selecta of Elliott H. Lieb. 4th ed. Zbl 1165.01331Lieb, Elliott H. 4 2005 A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002Carlen, E. A.; Lieb, E. H.; Loss, M. 47 2004 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303Lieb, Elliott H.; Solovej, Jan Philip 30 2004 Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313Lieb, Elliott H.; Seiringer, Robert 23 2004 One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 19 2004 A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070Lieb, Elliott H.; Loss, Michael 13 2004 Quantum mechanics, the stability of matter and quantum electrodynamics. Zbl 1255.81002Lieb, Elliott H. 3 2004 The stability of matter and quantum electrodynamics. Zbl 1081.81566Lieb, Elliott H. 2 2004 A short appreciation of Freeman Dyson’s long career in mathematical physics. Zbl 1101.01315Lieb, Elliott 1 2004 Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080Lieb, Elliott H.; Loss, Michael 36 2003 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107Lieb, Elliott H.; Seiringer, Robert 27 2003 Poincaré inequalities in punctured domains. Zbl 1048.26012Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 14 2003 The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009Lieb, Elliott H.; Wu, F. Y. 13 2003 The entropy of classical thermodynamics. Zbl 1163.80300Lieb, Elliott H.; Yngvason, Jakob 2 2003 Ground state energy of the one-component charged Bose gas. Zbl 1042.82004Lieb, Elliott H.; Solovej, Jan Philip 33 2002 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040Lieb, Elliott H.; Loss, Michael 18 2002 Stability of a model of relativistic quantum electrodynamics. Zbl 1005.81091Lieb, Elliott H.; Loss, Michael 11 2002 Segregation in the Falicov-Kimball model. Zbl 1004.82009Freericks, James K.; Lieb, Elliott H.; Ueltschi, Daniel 8 2002 Convex multivariable trace functions. Zbl 1034.46050Lieb, Elliott H.; Pedersen, Gert K. 7 2002 Inequalities. Selecta of Elliott H. Lieb. Edited, with a preface and commentaries by M. Loss and M. B. Ruskai. Zbl 1159.01356Lieb, Elliott H. 3 2002 Analysis. 2nd ed. Zbl 0966.26002Lieb, Elliott H.; Loss, Michael 790 2001 Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael 104 2001 A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 72 2001 ...and 120 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,282 Authors 108 Lieb, Elliott Hershel 81 Frank, Rupert L. 67 Seiringer, Robert 52 Solovej, Jan Philip 49 Lewin, Mathieu 45 Tang, Xianhua 40 Yang, Minbo 38 Loss, Michael 37 Fröhlich, Jürg Martin 37 Wu, Tsungfang 34 Carlen, Eric Anders 33 Alves, Claudianor Oliveira 33 Schlein, Benjamin 32 Dolbeault, Jean 32 Laptev, Ari 31 Ambrosio, Vincenzo 31 Phan Thành Nam 31 Rădulescu, Vicenţiu D. 30 Chen, Sitong 30 Rougerie, Nicolas 29 Hainzl, Christian 29 Peng, Shuangjie 28 Van Schaftingen, Jean 27 Siedentop, Heinz Karl Heinrich 27 Zou, Wenming 26 Deng, Yinbin 25 Chen, Jianqing 24 Squassina, Marco 23 Brézis, Haïm 23 Fournais, Søren 23 Miyagaki, Olimpio Hiroshi 23 Simon, Barry 22 Erdős, László 21 Lei, Yutian 21 Lions, Pierre-Louis 21 Lu, Guozhen 20 Bach, Volker 20 Figueiredo, Giovany Malcher 20 Pucci, Patrizia 20 Salani, Paolo 20 Sreenadh, Konijeti 19 Chen, Thomas M. 19 Naor, Assaf 19 Petz, Dénes 19 Ruskai, Mary Beth 19 Sun, Juntao 19 Yau, Horng-Tzer 19 Yngvason, Jakob 18 Hiroshima, Fumio 18 Miyao, Tadahiro 18 Xue, Kang 17 Benguria, Rafael D. 17 Carrillo de la Plata, José Antonio 17 Hansen, Frank-Peter 17 Hiai, Fumio 17 Sigal, Israel Michael 17 Spohn, Herbert 17 Xiao, Jie 16 Cao, Daomin 16 Chen, Caisheng 16 Chen, Haibo 16 Griesemer, Marcel 16 Hsu, TsingSan 16 Li, Congming 16 Nachtergaele, Bruno 16 Nguyễn Văn Hoàng 16 Wang, Zhi-Qiang 16 Yang, Jianfu 16 Zhang, Binlin 15 Esteban, Maria J. 15 Faupin, Jérémy 15 Fiscella, Alessio 15 Gao, Fashun 15 Serfaty, Sylvia 14 Bez, Neal 14 Guo, Yujin 14 Ilyin, Alexei A. 14 Li, Gongbao 14 Suragan, Durvudkhan 14 Tintarev, Kyril 14 Vazquez, Juan Luis 13 Csikvári, Péter 13 Dou, Jingbo 13 Hajaiej, Hichem 13 He, Xiaoming 13 Helffer, Bernard 13 Lei, Chunyu 13 Lenzmann, Enno 13 Liang, Sihua 13 Lü, Dengfeng 13 Mironescu, Petru 13 Peral Alonso, Ireneo 13 Slavnov, Nikita A. 13 Tang, Chunlei 13 Tasaki, Hal 13 Vugal’ter, Semën Abramovich 12 Bobkov, Sergey Germanovich 12 Bonheure, Denis 12 Cianchi, Andrea 12 Correggi, Michele ...and 6,182 more Authors all top 5 Cited in 576 Serials 400 Journal of Mathematical Physics 387 Communications in Mathematical Physics 270 Journal of Mathematical Analysis and Applications 264 Journal of Functional Analysis 235 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 215 Journal of Differential Equations 201 Calculus of Variations and Partial Differential Equations 199 Journal of Statistical Physics 111 Archive for Rational Mechanics and Analysis 110 Advances in Mathematics 106 Letters in Mathematical Physics 105 Annales Henri Poincaré 93 Linear Algebra and its Applications 86 Proceedings of the American Mathematical Society 84 Journal of Statistical Mechanics: Theory and Experiment 79 Transactions of the American Mathematical Society 75 Communications in Partial Differential Equations 75 Communications on Pure and Applied Analysis 74 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 72 Discrete and Continuous Dynamical Systems 70 Communications in Contemporary Mathematics 64 The Journal of Geometric Analysis 61 Reviews in Mathematical Physics 52 ZAMP. Zeitschrift für angewandte Mathematik und Physik 49 Advanced Nonlinear Studies 46 Journal de Mathématiques Pures et Appliquées. Neuvième Série 44 Applied Mathematics Letters 43 Annali di Matematica Pura ed Applicata. Serie Quarta 42 Potential Analysis 40 Boundary Value Problems 40 Journal of Physics A: Mathematical and Theoretical 38 SIAM Journal on Mathematical Analysis 37 Nonlinear Analysis. Theory, Methods & Applications 36 International Journal of Modern Physics B 36 Mathematische Annalen 36 Comptes Rendus. Mathématique. Académie des Sciences, Paris 36 Complex Variables and Elliptic Equations 36 Advances in Nonlinear Analysis 34 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 34 Journal of High Energy Physics 33 Duke Mathematical Journal 32 Applicable Analysis 32 Theoretical and Mathematical Physics 30 Discrete Mathematics 30 The Annals of Probability 30 NoDEA. Nonlinear Differential Equations and Applications 30 Journal of the European Mathematical Society (JEMS) 30 Science China. Mathematics 29 Computers & Mathematics with Applications 29 International Journal of Theoretical Physics 29 Nuclear Physics. B 29 Quantum Information Processing 27 Mathematische Zeitschrift 26 Inventiones Mathematicae 26 Manuscripta Mathematica 25 Journal of Combinatorial Theory. Series A 25 Bulletin of the American Mathematical Society. New Series 25 Journal of Mathematical Sciences (New York) 24 Communications on Pure and Applied Mathematics 24 Journal d’Analyse Mathématique 23 Nonlinearity 22 Probability Theory and Related Fields 22 Topological Methods in Nonlinear Analysis 22 Abstract and Applied Analysis 21 Journal of Computational Physics 21 Mathematical Methods in the Applied Sciences 21 New Journal of Physics 21 Acta Mathematica Sinica. English Series 21 Mediterranean Journal of Mathematics 20 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 20 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 19 Applied Mathematics and Computation 19 Acta Applicandae Mathematicae 19 Mathematical Physics, Analysis and Geometry 18 Reports on Mathematical Physics 18 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 18 Physical Review Letters 18 Acta Mathematica Scientia. Series B. (English Edition) 17 Discrete Applied Mathematics 17 Annales de l’Institut Fourier 17 Journal of Algebra 17 Monatshefte für Mathematik 17 Revista Matemática Iberoamericana 17 Annales de l’Institut Henri Poincaré. Physique Théorique 17 Nonlinear Analysis. Real World Applications 17 Milan Journal of Mathematics 17 Discrete and Continuous Dynamical Systems. Series S 16 Journal of the American Mathematical Society 16 Stochastic Processes and their Applications 16 St. Petersburg Mathematical Journal 16 Journal of Inequalities and Applications 16 International Journal of Quantum Information 16 Analysis and Mathematical Physics 16 Bulletin of Mathematical Sciences 16 Journal of Function Spaces 15 Rocky Mountain Journal of Mathematics 15 Mathematische Nachrichten 15 Physica D 15 The Journal of Fourier Analysis and Applications 15 Infinite Dimensional Analysis, Quantum Probability and Related Topics ...and 476 more Serials all top 5 Cited in 62 Fields 3,465 Partial differential equations (35-XX) 1,599 Quantum theory (81-XX) 1,254 Statistical mechanics, structure of matter (82-XX) 765 Functional analysis (46-XX) 719 Operator theory (47-XX) 504 Probability theory and stochastic processes (60-XX) 445 Calculus of variations and optimal control; optimization (49-XX) 412 Real functions (26-XX) 412 Global analysis, analysis on manifolds (58-XX) 299 Combinatorics (05-XX) 238 Information and communication theory, circuits (94-XX) 214 Linear and multilinear algebra; matrix theory (15-XX) 209 Harmonic analysis on Euclidean spaces (42-XX) 201 Differential geometry (53-XX) 198 Convex and discrete geometry (52-XX) 198 Fluid mechanics (76-XX) 150 Integral equations (45-XX) 139 Numerical analysis (65-XX) 114 Dynamical systems and ergodic theory (37-XX) 109 Group theory and generalizations (20-XX) 108 Potential theory (31-XX) 99 Ordinary differential equations (34-XX) 88 Measure and integration (28-XX) 82 Optics, electromagnetic theory (78-XX) 74 Statistics (62-XX) 71 Associative rings and algebras (16-XX) 63 Biology and other natural sciences (92-XX) 62 Relativity and gravitational theory (83-XX) 61 Difference and functional equations (39-XX) 61 Mechanics of deformable solids (74-XX) 59 Operations research, mathematical programming (90-XX) 56 Nonassociative rings and algebras (17-XX) 56 Abstract harmonic analysis (43-XX) 54 Manifolds and cell complexes (57-XX) 52 Astronomy and astrophysics (85-XX) 51 Special functions (33-XX) 51 Mechanics of particles and systems (70-XX) 50 Computer science (68-XX) 47 Topological groups, Lie groups (22-XX) 46 Functions of a complex variable (30-XX) 44 Number theory (11-XX) 41 Classical thermodynamics, heat transfer (80-XX) 38 Several complex variables and analytic spaces (32-XX) 37 Integral transforms, operational calculus (44-XX) 25 Approximations and expansions (41-XX) 21 Category theory; homological algebra (18-XX) 19 Systems theory; control (93-XX) 18 Geometry (51-XX) 18 General topology (54-XX) 17 History and biography (01-XX) 16 Order, lattices, ordered algebraic structures (06-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 General and overarching topics; collections (00-XX) 13 Algebraic topology (55-XX) 11 Commutative algebra (13-XX) 9 Mathematical logic and foundations (03-XX) 9 Geophysics (86-XX) 8 Algebraic geometry (14-XX) 6 Sequences, series, summability (40-XX) 4 General algebraic systems (08-XX) 3 Mathematics education (97-XX) 2 Field theory and polynomials (12-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.