Edit Profile (opens in new tab) Lieb, Elliott Hershel Co-Author Distance 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) · Kyoto Prize in Basic Sciences (2023) Documents Indexed: 260 Publications since 1957, including 11 Books 1 Contribution as Editor · 2 Further Contributions Biographic References: 12 Publications Co-Authors: 80 Co-Authors with 203 Joint Publications 2,710 Co-Co-Authors all top 5 Co-Authors 56 single-authored 38 Seiringer, Robert 32 Frank, Rupert L. 29 Yngvason, Jakob 27 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 Lewin, Mathieu 5 Thomas, Lawrence E. 4 Giuliani, Alessandro 4 Lebowitz, Joel Louis 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 Matthew 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 13 Journal of Mathematical Physics 11 Journal of Statistical Physics 9 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 109 Quantum theory (81-XX) 81 Statistical mechanics, structure of matter (82-XX) 53 Partial differential equations (35-XX) 42 Functional analysis (46-XX) 25 Operator theory (47-XX) 24 Real functions (26-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 16 Information and communication theory, circuits (94-XX) 13 History and biography (01-XX) 13 Probability theory and stochastic processes (60-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Measure and integration (28-XX) 6 General and overarching topics; collections (00-XX) 6 Combinatorics (05-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 Order, lattices, ordered algebraic structures (06-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 Numerical analysis (65-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 222 Publications have been cited 11,467 times in 8,096 Documents Cited by ▼ Year ▼ A relation between pointwise convergence of functions and convergence of functionals. Zbl 0526.46037Brézis, Haïm; Lieb, Elliott H. 1,235 1983 Analysis. 2nd ed. Zbl 0966.26002Lieb, Elliott H.; Loss, Michael 1,109 2001 Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Zbl 0527.42011Lieb, Elliott H. 667 1983 Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Zbl 0369.35022Lieb, Elliott H. 554 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. 397 1976 Two soluble models of an antiferromagnetic chain. Zbl 0129.46401Lieb, Elliott H.; Schultz, Theodore; Mattis, D. 312 1961 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. 310 1971 Exact analysis of an interaction Bose gas. I: The general solution and the ground state. Zbl 0138.23001Lieb, Elliott H.; Liniger, Werner 239 1963 Theory of monomer-dimer systems. Zbl 0228.05131Heilmann, Ole J.; Lieb, Elliott H. 237 1972 The mathematics of the Bose gas and its condensation. Zbl 1104.82012Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 215 2005 Convex trace functions and the Wigner-Yanase-Dyson conjecture. Zbl 0267.46055Lieb, Elliott H. 215 1973 Harmonic maps with defects. Zbl 0608.58016Brézis, Haïm; Coron, Jean-Michel; Lieb, Elliott H. 200 1986 The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568Lieb, Elliott H.; Simon, Barry 193 1977 The Chandrasekhar theory of stellar collapse as the limit quantum mechanics. Zbl 0641.35065Lieb, Elliott H.; Yau, Horng-Tzer 179 1987 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. 179 1976 Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Zbl 0339.26020Brascamp, Herm Jan; Lieb, Elliott H. 162 1976 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 157 2008 The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Zbl 0478.49035Benguria, Rafael; Brézis, Haïm; Lieb, Elliott H. 157 1981 Sharp uniform convexity and smoothness inequalities for trace norms. Zbl 0803.47037Ball, Keith; Carlen, Eric A.; Lieb, Elliott H. 144 1994 A general rearrangement inequality for multiple integrals. Zbl 0286.26005Brascamp, H. J.; Lieb, Elliott H.; Luttinger, J. M. 138 1974 Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014Almgren, Frederick J. jun.; Lieb, Elliott H. 128 1989 Bounds on the eigenvalues of the Laplace and Schrödinger operators. Zbl 0329.35018Lieb, Elliott H. 123 1976 On the lowest eigenvalue of the Laplacian for the intersection of two domains. Zbl 0538.35058Lieb, Elliott H. 114 1983 The classical limit of quantum spin systems. Zbl 1125.82305Lieb, Elliott H. 109 1973 Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael 107 2001 Thomas-Fermi and related theories of atoms and molecules. Zbl 1114.81336Lieb, Elliott H. 104 1981 The stability of matter in quantum mechanics. Zbl 1179.81004Lieb, Elliott H.; Seiringer, Robert 102 2009 Gaussian kernels have only Gaussian maximizers. Zbl 0726.42005Lieb, Elliott H. 99 1990 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 92 2012 Minimum action solutions of some vector field equations. Zbl 0579.35025Brézis, Haïm; Lieb, Elliott H. 89 1984 Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004Lieb, Elliott H.; Seiringer, Robert 88 2006 The stability and instability of relativistic matter. Zbl 0686.35099Lieb, Elliott H.; Yau, Horng-Tzer 86 1988 Thomas-Fermi and related theories of atoms and molecules. Zbl 1049.81679Lieb, Elliott H. 84 1981 Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip 80 1994 Sobolev inequalities with remainder terms. Zbl 0577.46031Brézis, Haïm; Lieb, Elliott H. 78 1985 A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 78 2001 Proof of an entropy conjecture of Wehrl. Zbl 0385.60089Lieb, Elliott H. 73 1978 Exact analysis of an interacting Bose gas. II: The excitation spectrum. Zbl 0138.23002Lieb, Elliott H. 72 1963 Stability of Coulomb systems with magnetic fields. I: The one-electron atom. Zbl 0595.35098Fröhlich, Jürg; Lieb, Elliott H.; Loss, Michael 71 1986 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 71 2013 Analysis. Zbl 0873.26002Lieb, Elliott H.; Loss, Michael 65 1996 The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei. Zbl 1049.82501Lieb, Eliott H.; Lebowitz, Joel L. 62 1972 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 60 2010 Integral bounds for radar ambiguity functions and Wigner distributions. Zbl 0704.46050Lieb, Elliott H. 60 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. 53 2004 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 51 2006 The physics and mathematics of the second law of thermodynamics. Zbl 1027.80504Lieb, Elliott H.; Yngvason, Jakob 51 1999 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 47 2012 Some operator inequalities of the Schwarz type. Zbl 0274.46045Lieb, Elliott H.; Ruskai, Mary Beth 47 1974 Exact ground state energy of the strong-coupling polaron. Zbl 0874.60095Lieb, Elliott H.; Thomas, Lawrence E. 46 1997 The stability of matter: From atoms to stars. Zbl 0698.35135Lieb, Elliott H. 45 1990 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 43 1996 Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma. Zbl 0348.26011Brascamp, H. J.; Lieb, Elliott H. 41 1975 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015Carlen, Eric A.; Lieb, Elliott H. 40 2008 On characteristic exponents in turbulence. Zbl 0598.76054Lieb, Elliott H. 40 1984 Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions. Zbl 0807.47058Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob 40 1994 Ground state energy of the one-component charged Bose gas. Zbl 1042.82004Lieb, Elliott H.; Solovej, Jan Philip 40 2002 The ground state energy and density of interacting bosons in a trap. Zbl 1043.82515Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 39 2000 A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Zbl 0929.34076Hundertmark, Dirk; Lieb, Elliott H.; Thomas, Lawrence E. 39 1998 Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080Lieb, Elliott H.; Loss, Michael 37 2003 Some convexity and subadditivity properties of entropy. Zbl 0308.94020Lieb, Elliott H. 37 1975 The ground state energy of a dilute two-dimensional Bose gas. Zbl 1115.82306Lieb, Elliott H.; Yngvason, Jakob 37 2001 Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities. Zbl 0796.46054Carlen, Eric A.; Lieb, Elliott H. 36 1993 Proofs of some conjectures on permanents. Zbl 0144.26802Lieb, Elliott H. 36 1966 Ordering energy levels of interacting spin systems. Zbl 0101.45302Lieb, Elliott H.; Mattis, Daniel 34 1962 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 33 2015 Concavity properties and a generating function for Stirling numbers. Zbl 0164.33002Lieb, Elliott H. 33 1968 Long range atomic potentials in Thomas-Fermi theory. Zbl 0416.35066Brézis, Haïm; Lieb, Elliott H. 32 1979 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303Lieb, Elliott H.; Solovej, Jan Philip 31 2004 Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013Almgren, Frederick J. jun.; Lieb, Elliot H. 30 1988 Fluxes, Laplacians, and Kasteleyn’s theorem. Zbl 0787.05083Lieb, Elliott H.; Loss, Michael 30 1993 One-electron relativistic molecules with Coulomb interaction. Zbl 0946.81522Daubechies, Ingrid; Lieb, Elliott H. 29 1983 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 28 2014 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107Lieb, Elliott H.; Seiringer, Robert 28 2003 The thermodynamic limit for jellium. Zbl 0973.82500Lieb, Elliott H.; Narnhofer, Heide 27 1975 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 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 25 2014 Stability of matter in magnetic fields. Zbl 1020.81957Lieb, Elliott H.; Loss, Michael; Solovej, Jan Philip 25 1995 An itinerant electron model with crystalline or magnetic long range order. Zbl 1002.82508Kennedy, Tom; Lieb, Elliott H. 24 1986 Ground-state energy and effective mass of the polaron. Zbl 0100.42504Lieb, Elliott H.; Yamazaki, Kazuo 24 1958 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 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 22 2013 Studies in mathematical physics. Essays in honor of Valentine Bargmann. Zbl 0326.00007 21 1976 The number of bound states of one-body Schrödinger operators and the Weyl problem. Zbl 0445.58029Lieb, Elliott H. 21 1980 The local density approximation in density functional theory. Zbl 1435.35320Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 21 2020 One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 20 2004 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040Lieb, Elliott H.; Loss, Michael 19 2002 Theory of ferromagnetism and the ordering of electronic energy levels. Zbl 0118.46202Lieb, Elliott H.; Mattis, D. 19 1962 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116Lieb, Elliott H.; Solovej, Jan Philip 18 2014 A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070Lieb, Elliott H.; Loss, Michael 17 2004 An inequality of Hadamard type for permanents. Zbl 1116.15015Carlen, Eric; Lieb, Elliott H.; Loss, Michael 17 2006 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 17 2016 A guide to entropy and second law of thermodynamics. Zbl 1038.80504Lieb, Elliott H.; Yngvason, Jakob 17 1998 A Minkowski type trace inequality and strong subadditivity of quantum entropy. Zbl 0933.47014Carlen, Eric A.; Lieb, Elliott H. 17 1999 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 16 2009 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 16 2011 Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216Lieb, Elliott H.; Yang, Yisong 16 2012 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. 16 2018 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020Frank, Rupert L.; Lieb, Elliott H. 8 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 4 2021 Inequalities for \(L^p\)-norms that sharpen the triangle inequality and complement Hanner’s inequality. Zbl 1475.46028Carlen, Eric A.; Frank, Rupert L.; Ivanisvili, Paata; Lieb, Elliott H. 3 2021 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. 2 2021 The local density approximation in density functional theory. Zbl 1435.35320Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 21 2020 Divergence of the effective mass of a polaron in the strong coupling limit. Zbl 1446.81045Lieb, Elliott H.; Seiringer, Robert 9 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 8 2019 Some trace inequalities for exponential and logarithmic functions. Zbl 1476.15034Carlen, Eric A.; Lieb, Elliott H. 3 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. 16 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 14 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 11 2018 Rigidity of the Laughlin liquid. Zbl 1398.81326Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob 7 2018 Nematic liquid crystal phase in a system of interacting dimers and monomers. Zbl 1400.82320Jauslin, Ian; Lieb, Elliott H. 3 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 17 2016 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 13 2016 A Pfaffian formula for monomer-dimer partition functions. Zbl 1342.82161Giuliani, Alessandro; Jauslin, Ian; Lieb, Elliott H. 5 2016 Entropy and entanglement bounds for reduced density matrices of fermionic states. Zbl 1342.81031Carlen, Eric A.; Lieb, Elliott H.; Reuvers, Robin 4 2016 Proof of the Wehrl-type entropy conjecture for symmetric \({SU(N)}\) coherent states. Zbl 1365.81030Lieb, Elliott H.; Solovej, Jan Philip 3 2016 On a quantum entropy power inequality of Audenaert, Datta, and Ozols. Zbl 1341.81015Carlen, Eric A.; Lieb, Elliott H.; Loss, Michael 3 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. 33 2015 Columnar phase in quantum dimer models. Zbl 1320.82011Giuliani, Alessandro; Lieb, Elliott H. 2 2015 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 28 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 25 2014 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116Lieb, Elliott H.; Solovej, Jan Philip 18 2014 Remainder terms for some quantum entropy inequalities. Zbl 1292.81021Carlen, Eric A.; Lieb, Elliott H. 15 2014 Formation of stripes and slabs near the ferromagnetic transition. Zbl 1302.82018Giuliani, Alessandro; Lieb, Elliott H.; Seiringer, Robert 8 2014 Equivalence of two definitions of the effective mass of a polaron. Zbl 1295.81055Lieb, Elliott H.; Seiringer, Robert 7 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 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 4 2014 Entropy meters and the entropy of non-extensive systems. Zbl 1371.80005Lieb, Elliott H.; Yngvason, Jakob 4 2014 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 71 2013 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 22 2013 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 10 2013 The entropy concept for non-equilibrium states. Zbl 1371.80004Lieb, Elliott H.; Yngvason, Jakob 9 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 On an extension problem for density matrices. Zbl 1282.81020Carlen, Eric A.; Lebowitz, Joel L.; Lieb, Elliott H. 4 2013 A smooth complex generalization of the Hobby-Rice theorem. Zbl 1295.41025Lazarev, Oleg; Lieb, Elliott H. 4 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 3 2013 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 92 2012 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 47 2012 Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216Lieb, Elliott H.; Yang, Yisong 16 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. 9 2012 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 5 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. 16 2011 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013Frank, Rupert L.; Lieb, Elliott H. 7 2011 Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 3 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 60 2010 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 14 2010 Localization of multidimensional Wigner distributions. Zbl 1314.81129Lieb, Elliott H.; Ostrover, Yaron 5 2010 The stability of matter in quantum mechanics. Zbl 1179.81004Lieb, Elliott H.; Seiringer, Robert 102 2009 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 16 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. 15 2009 Symmetry breaking in Laughlin’s state on a cylinder. Zbl 1155.81032Jansen, S.; Lieb, E. H.; Seiler, R. 9 2009 Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. Zbl 1190.15009Carlen, Eric A.; Lieb, Elliott H. 4 2009 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 157 2008 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015Carlen, Eric A.; Lieb, Elliott H. 40 2008 Brascamp–Lieb inequalities for non-commutative integration. Zbl 1173.46045Carlen, Eric A.; Lieb, Elliott H. 3 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 15 2007 Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 6 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 88 2006 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 51 2006 An inequality of Hadamard type for permanents. Zbl 1116.15015Carlen, Eric; Lieb, Elliott H.; Loss, Michael 17 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. 15 2006 Ground-state energy of a dilute Fermi gas. Zbl 1114.82004Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip 4 2006 Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V. 3 2006 Some matrix rearrangement inequalities. Zbl 1197.15011Carlen, Eric; Lieb, Elliott H. 2 2006 The mathematics of the Bose gas and its condensation. Zbl 1104.82012Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 215 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 6 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. 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 A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002Carlen, E. A.; Lieb, E. H.; Loss, M. 53 2004 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303Lieb, Elliott H.; Solovej, Jan Philip 31 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 20 2004 A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070Lieb, Elliott H.; Loss, Michael 17 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 37 2003 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107Lieb, Elliott H.; Seiringer, Robert 28 2003 The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009Lieb, Elliott H.; Wu, F. Y. 14 2003 Poincaré inequalities in punctured domains. Zbl 1048.26012Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 14 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 40 2002 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040Lieb, Elliott H.; Loss, Michael 19 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 9 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 1,109 2001 ...and 122 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,181 Authors 111 Lieb, Elliott Hershel 88 Frank, Rupert L. 76 Seiringer, Robert 54 Solovej, Jan Philip 52 Lewin, Mathieu 52 Tang, Xianhua 48 Yang, Minbo 45 Schlein, Benjamin 42 Tang, Chun-Lei 40 Rădulescu, Vicenţiu D. 39 Carlen, Eric Anders 39 Loss, Michael 39 Wu, Tsungfang 38 Fröhlich, Jürg Martin 35 Alves, Claudianor Oliveira 35 Chen, Haibo 35 Laptev, Ari 34 Ambrosio, Vincenzo 34 Phan Thành Nam 33 Dolbeault, Jean 33 Rougerie, Nicolas 32 Chen, Sitong 32 Zou, Wenming 30 Hainzl, Christian 30 Peng, Shuangjie 30 Van Schaftingen, Jean 29 Deng, Yinbin 28 Siedentop, Heinz Karl Heinrich 27 Chen, Jianqing 26 Squassina, Marco 25 Miyagaki, Olimpio Hiroshi 24 Fournais, Søren 24 Lu, Guozhen 24 Simon, Barry 23 Brézis, Haïm 23 Erdős, László 23 Lei, Yutian 21 Lions, Pierre-Louis 21 Salani, Paolo 21 Sreenadh, Konijeti 21 Sun, Juntao 21 Zhang, Binlin 20 Bach, Volker 20 Carrillo de la Plata, José Antonio 20 Figueiredo, Giovany Malcher 20 Naor, Assaf 20 Pucci, Patrizia 20 Ruskai, Mary Beth 19 Chen, Thomas 19 Nachtergaele, Bruno 19 Petz, Dénes 19 Xiao, Jie 19 Yau, Horng-Tzer 19 Yngvason, Jakob 18 Cao, Daomin 18 Fiscella, Alessio 18 Guo, Yujin 18 Hiroshima, Fumio 18 Lei, Chunyu 18 Miyao, Tadahiro 18 Sigal, Israel Michael 18 Wang, Zhi-Qiang 18 Xue, Kang 18 Yang, Jianfu 17 Benguria, Rafael D. 17 Chen, Caisheng 17 Gao, Fashun 17 Hajaiej, Hichem 17 Hansen, Frank-Peter 17 Hiai, Fumio 17 Hsu, TsingSan 17 Spohn, Herbert 16 Griesemer, Marcel 16 Li, Congming 16 Liang, Sihua 16 Nguyễn Văn Hoàng 16 Serfaty, Sylvia 16 Suragan, Durvudkhan 16 Vugal’ter, Semën Abramovich 15 Bez, Neal 15 Csikvári, Péter 15 Dou, Jingbo 15 Esteban, Maria J. 15 Faupin, Jérémy 15 Ilyin, Alexei A. 15 Jeanjean, Louis 15 Li, Gongbao 15 Liao, Jiafeng 15 Ruzhansky, Michael V. 15 Tasaki, Hal 15 Tintarev, Kyril 15 Wang, Jun 14 He, Xiaoming 14 Kovařík, Hynek 14 Lenzmann, Enno 14 Liu, Zhisu 14 Peral Alonso, Ireneo 14 Slavnov, Nikita A. 14 Vazquez, Juan Luis 13 Bobkov, Sergey Germanovich ...and 7,081 more Authors all top 5 Cited in 613 Serials 431 Journal of Mathematical Physics 400 Communications in Mathematical Physics 303 Journal of Mathematical Analysis and Applications 290 Journal of Functional Analysis 245 Journal of Differential Equations 245 Nonlinear Analysis. 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