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: 291 Publications since 1957, including 11 Books and 31 Additional arXiv Preprints 1 Contribution as Editor · 3 Further Contributions Biographic References: 12 Publications Co-Authors: 85 Co-Authors with 233 Joint Publications 3,051 Co-Co-Authors all top 5 Co-Authors 58 single-authored 51 Seiringer, Robert 37 Frank, Rupert L. 34 Yngvason, Jakob 28 Carlen, Eric Anders 25 Solovej, Jan Philip 24 Loss, Michael 12 Almgren, Frederick Justin jun. 9 Giuliani, Alessandro 9 Lewin, Mathieu 8 Lebowitz, Joel Louis 8 Siedentop, Heinz Karl Heinrich 7 Brézis, Haïm 6 Brascamp, Herm Jan 6 Jauslin, Ian 6 Thomas, Lawrence E. 4 Aizenman, Michael 4 Nachtergaele, Bruno 4 Simon, Barry 3 Bach, Volker 3 Heilmann, Ole J. 3 Mattis, Daniel Charles 3 Yau, Horng-Tzer 2 Benguria, Rafael D. 2 Coron, Jean-Michel 2 Daubechies, Ingrid Chantal 2 Freericks, James K. 2 Jaffe, Arthur Michael 2 Liniger, Werner 2 McCann, Robert J. 2 Narnhofer, Heide 2 Rougerie, Nicolas 2 Ruelle, David Pierre 2 Ruskai, Mary Beth 2 Schupp, Peter 2 Ueltschi, Daniel 2 Vershynina, Anna 2 Wightman, Arthur Strong 1 Almgren, Robert F. 1 Ball, Keith Martin 1 Barnes, John F. 1 Barnsley, Michael Fielding 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 Connes, Alain 1 Cordero-Erausquin, Dario 1 Davies, Edward Brian 1 Decker, Colin 1 DeWitt-Morette, Cécile 1 Eisenberg, Eli 1 Epstein, David Bernard Alper 1 Epstein, Henri 1 Evans, David E. 1 Fellbaum, Christiane 1 Flato, Moshé 1 Fröhlich, Jürg Martin 1 Gallavotti, Giovanni M. 1 Ginibre, Jean 1 Glaser, Vladimir Jurko 1 Glashow, Sheldon Lee 1 Glimm, James G. 1 Griesemer, Marcel 1 Griffiths, Robert B. 1 Hepp, Klaus 1 Hundertmark, Dirk 1 Iantchenko, Alexei 1 Ivanisvili, Paata 1 Jansen, Sabine 1 Jerison, David S. 1 Jørgensen, Palle E. T. 1 Kennedy, Tom 1 Kishimoto, Aki 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 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 Sabin, Julien 1 Sakakura, A. Y. 1 Sanches Fernandes, K. 1 Schrader, Robert 1 Schultz, Theodore 1 Seiler, Ruedi ...and 14 more Co-Authors 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 Notices of the American Mathematical Society 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 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 112 Quantum theory (81-XX) 84 Statistical mechanics, structure of matter (82-XX) 53 Partial differential equations (35-XX) 42 Functional analysis (46-XX) 26 Operator theory (47-XX) 24 Real functions (26-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 17 Information and communication theory, circuits (94-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 14 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 Topological groups, Lie groups (22-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 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 227 Publications have been cited 12,514 times in 8,803 Documents Cited by ▼ Year ▼ Analysis. 2nd ed. Zbl 0966.26002 Lieb, Elliott H.; Loss, Michael 1,409 2001 A relation between pointwise convergence of functions and convergence of functionals. Zbl 0526.46037 Brézis, Haïm; Lieb, Elliott H. 1,341 1983 Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Zbl 0527.42011 Lieb, Elliott H. 715 1983 Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation. Zbl 0369.35022 Lieb, Elliott H. 625 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 0334.26009 Brascamp, Herm Jan; Lieb, Elliott H. 423 1976 Two soluble models of an antiferromagnetic chain. Zbl 0129.46401 Lieb, Elliott H.; Schultz, Theodore; Mattis, D. 329 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 0211.56703 Temperley, H. V. N.; Lieb, Elliott H. 327 1971 Exact analysis of an interaction Bose gas. I: The general solution and the ground state. Zbl 0138.23001 Lieb, Elliott H.; Liniger, Werner 259 1963 Theory of monomer-dimer systems. Zbl 0228.05131 Heilmann, Ole J.; Lieb, Elliott H. 248 1972 Convex trace functions and the Wigner-Yanase-Dyson conjecture. Zbl 0267.46055 Lieb, Elliott H. 229 1973 The mathematics of the Bose gas and its condensation. Zbl 1104.82012 Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 227 2005 Harmonic maps with defects. Zbl 0608.58016 Brézis, Haïm; Coron, Jean-Michel; Lieb, Elliott H. 208 1986 The Thomas-Fermi theory of atoms, molecules and solids. Zbl 0938.81568 Lieb, Elliott H.; Simon, Barry 200 1977 Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Zbl 0342.35044 Lieb, Elliott H.; Thirring, Walter E. 190 1976 The Chandrasekhar theory of stellar collapse as the limit quantum mechanics. Zbl 0641.35065 Lieb, Elliott H.; Yau, Horng-Tzer 189 1987 The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Zbl 0478.49035 Benguria, Rafael; Brézis, Haïm; Lieb, Elliott H. 175 1981 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 175 2008 Best constants in Young’s inequality, its converse, and its generalization to more than three functions. Zbl 0339.26020 Brascamp, Herm Jan; Lieb, Elliott H. 172 1976 Sharp uniform convexity and smoothness inequalities for trace norms. Zbl 0803.47037 Ball, Keith; Carlen, Eric A.; Lieb, Elliott H. 150 1994 Symmetric decreasing rearrangement is sometimes continuous. Zbl 0688.46014 Almgren, Frederick J. jun.; Lieb, Elliott H. 145 1989 A general rearrangement inequality for multiple integrals. Zbl 0286.26005 Brascamp, H. J.; Lieb, Elliott H.; Luttinger, J. M. 142 1974 Bounds on the eigenvalues of the Laplace and Schrödinger operators. Zbl 0329.35018 Lieb, Elliott H. 128 1976 On the lowest eigenvalue of the Laplacian for the intersection of two domains. Zbl 0538.35058 Lieb, Elliott H. 123 1983 The classical limit of quantum spin systems. Zbl 1125.82305 Lieb, Elliott H. 116 1973 Ground states in non-relativistic quantum electrodynamics. Zbl 1044.81133 Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael 113 2001 Thomas-Fermi and related theories of atoms and molecules. Zbl 1114.81336 Lieb, Elliott H. 112 1981 The stability of matter in quantum mechanics. Zbl 1179.81004 Lieb, Elliott H.; Seiringer, Robert 107 2009 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023 Frank, Rupert L.; Lieb, Elliott H. 106 2012 Gaussian kernels have only Gaussian maximizers. Zbl 0726.42005 Lieb, Elliott H. 101 1990 Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004 Lieb, Elliott H.; Seiringer, Robert 98 2006 Minimum action solutions of some vector field equations. Zbl 0579.35025 Brézis, Haïm; Lieb, Elliott H. 92 1984 Thomas-Fermi and related theories of atoms and molecules. Zbl 1049.81679 Lieb, Elliott H. 90 1981 The stability and instability of relativistic matter. Zbl 0686.35099 Lieb, Elliott H.; Yau, Horng-Tzer 87 1988 Sobolev inequalities with remainder terms. Zbl 0577.46031 Brézis, Haïm; Lieb, Elliott H. 85 1985 Generalized Hartree-Fock theory and the Hubbard model. Zbl 0839.60095 Bach, Volker; Lieb, Elliott H.; Solovej, Jan Philip 84 1994 A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Zbl 0996.82010 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 81 2001 Exact analysis of an interacting Bose gas. II: The excitation spectrum. Zbl 0138.23002 Lieb, Elliott H. 80 1963 Proof of an entropy conjecture of Wehrl. Zbl 0385.60089 Lieb, Elliott H. 79 1978 Monotonicity of a relative Rényi entropy. Zbl 1350.94020 Frank, Rupert L.; Lieb, Elliott H. 79 2013 Stability of Coulomb systems with magnetic fields. I: The one-electron atom. Zbl 0595.35098 Fröhlich, Jürg; Lieb, Elliott H.; Loss, Michael 72 1986 Analysis. Zbl 0873.26002 Lieb, Elliott H.; Loss, Michael 68 1996 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024 Frank, Rupert L.; Lieb, Elliott H. 65 2010 Integral bounds for radar ambiguity functions and Wigner distributions. Zbl 0704.46050 Lieb, Elliott H. 64 1990 The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei. Zbl 1049.82501 Lieb, Eliott H.; Lebowitz, Joel L. 62 1972 The physics and mathematics of the second law of thermodynamics. Zbl 1027.80504 Lieb, Elliott H.; Yngvason, Jakob 58 1999 A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002 Carlen, E. A.; Lieb, E. H.; Loss, M. 55 2004 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023 Frank, Rupert L.; Lieb, Elliott H. 54 2012 Exact ground state energy of the strong-coupling polaron. Zbl 0874.60095 Lieb, Elliott H.; Thomas, Lawrence E. 54 1997 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382 Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 52 2006 Some operator inequalities of the Schwarz type. Zbl 0274.46045 Lieb, Elliott H.; Ruskai, Mary Beth 49 1974 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005 Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 45 1996 The stability of matter: From atoms to stars. Zbl 0698.35135 Lieb, Elliott H. 45 1990 Asymptotics of heavy atoms in high magnetic fields. II: Semiclassical regions. Zbl 0807.47058 Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob 43 1994 Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma. Zbl 0348.26011 Brascamp, H. J.; Lieb, Elliott H. 42 1975 Ground state energy of the one-component charged Bose gas. Zbl 1042.82004 Lieb, Elliott H.; Solovej, Jan Philip 41 2002 A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Zbl 0929.34076 Hundertmark, Dirk; Lieb, Elliott H.; Thomas, Lawrence E. 41 1998 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015 Carlen, Eric A.; Lieb, Elliott H. 41 2008 On characteristic exponents in turbulence. Zbl 0598.76054 Lieb, Elliott H. 41 1984 The ground state energy and density of interacting bosons in a trap. Zbl 1043.82515 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 39 2000 The ground state energy of a dilute two-dimensional Bose gas. Zbl 1115.82306 Lieb, Elliott H.; Yngvason, Jakob 39 2001 Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080 Lieb, Elliott H.; Loss, Michael 37 2003 Some convexity and subadditivity properties of entropy. Zbl 0308.94020 Lieb, Elliott H. 37 1975 Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities. Zbl 0796.46054 Carlen, Eric A.; Lieb, Elliott H. 37 1993 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042 Frank, Rupert L.; Lieb, Elliott H. 37 2015 Ordering energy levels of interacting spin systems. Zbl 0101.45302 Lieb, Elliott H.; Mattis, Daniel 36 1962 Proofs of some conjectures on permanents. Zbl 0144.26802 Lieb, Elliott H. 36 1966 The number of bound states of one-body Schrödinger operators and the Weyl problem. Zbl 0445.58029 Lieb, Elliott H. 36 1980 Concavity properties and a generating function for Stirling numbers. Zbl 0164.33002 Lieb, Elliott H. 34 1968 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303 Lieb, Elliott H.; Solovej, Jan Philip 33 2004 Long range atomic potentials in Thomas-Fermi theory. Zbl 0416.35066 Brézis, Haïm; Lieb, Elliott H. 32 1979 Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds. Zbl 0673.58013 Almgren, Frederick J. jun.; Lieb, Elliot H. 31 1988 One-electron relativistic molecules with Coulomb interaction. Zbl 0946.81522 Daubechies, Ingrid; Lieb, Elliott H. 31 1983 Fluxes, Laplacians, and Kasteleyn’s theorem. Zbl 0787.05083 Lieb, Elliott H.; Loss, Michael 31 1993 Asymptotics of heavy atoms in high magnetic fields. I: Lowest Landau band regions. Zbl 0800.49041 Lieb, Elliott H.; Solovej, Jan Philip; Yngvason, Jakob 30 1994 The thermodynamic limit for jellium. Zbl 0973.82500 Lieb, Elliott H.; Narnhofer, Heide 29 1975 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 29 2014 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107 Lieb, Elliott H.; Seiringer, Robert 28 2003 Stability of matter in magnetic fields. Zbl 1020.81957 Lieb, Elliott H.; Loss, Michael; Solovej, Jan Philip 27 1995 Ground-state energy and effective mass of the polaron. Zbl 0100.42504 Lieb, Elliott H.; Yamazaki, Kazuo 27 1958 Strichartz inequality for orthonormal functions. Zbl 1307.35245 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 27 2014 Co-area, liquid crystals, and minimal surfaces. Zbl 0645.58015 Almgren, F.; Browder, W.; Lieb, E. H. 25 1988 Studies in mathematical physics. Essays in honor of Valentine Bargmann. Zbl 0326.00007 25 1976 An itinerant electron model with crystalline or magnetic long range order. Zbl 1002.82508 Kennedy, Tom; Lieb, Elliott H. 24 1986 Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313 Lieb, Elliott H.; Seiringer, Robert 23 2004 Stability of Coulomb systems with magnetic fields. II. The many-electron atom and the one-electron molecule. Zbl 0607.35082 Lieb, Elliott H.; Loss, Michael 23 1986 The local density approximation in density functional theory. Zbl 1435.35320 Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2020 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2013 One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 20 2004 Theory of ferromagnetism and the ordering of electronic energy levels. Zbl 0118.46202 Lieb, Elliott H.; Mattis, D. 19 1962 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023 Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 19 2016 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040 Lieb, Elliott H.; Loss, Michael 19 2002 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116 Lieb, Elliott H.; Solovej, Jan Philip 19 2014 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 18 2007 An inequality of Hadamard type for permanents. Zbl 1116.15015 Carlen, Eric; Lieb, Elliott H.; Loss, Michael 18 2006 Inequalities for some operator and matrix functions. Zbl 0324.15013 Lieb, Elliott H. 18 1976 Probabilistic coherence and proper scoring rules. Zbl 1367.94139 Predd, Joel B.; Seiringer, Robert; Lieb, Elliott H.; Osherson, Daniel N.; Poor, H. Vincent; Kulkarni, Sanjeev R. 18 2009 A guide to entropy and second law of thermodynamics. Zbl 1038.80504 Lieb, Elliott H.; Yngvason, Jakob 17 1998 A Minkowski type trace inequality and strong subadditivity of quantum entropy. Zbl 0933.47014 Carlen, Eric A.; Lieb, Elliott H. 17 1999 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008 Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 17 2009 A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070 Lieb, Elliott H.; Loss, Michael 17 2004 On the extension of the FKG inequality to \(n\) functions. Zbl 1507.06014 Lieb, Elliott H.; Sahi, Siddhartha 1 2022 A trace inequality of Ando, Hiai, and Okubo and a monotonicity property of the Golden-Thompson inequality. Zbl 1512.47028 Carlen, Eric A.; Lieb, Elliott H. 1 2022 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020 Frank, Rupert L.; Lieb, Elliott H. 10 2021 Wehrl-type coherent state entropy inequalities for \(\mathrm{SU}(1,1)\) and its \(AX+B\) subgroup. Zbl 1480.81064 Lieb, Elliott H.; Solovej, Jan Philip 7 2021 Inequalities for \(L^p\)-norms that sharpen the triangle inequality and complement Hanner’s inequality. Zbl 1475.46028 Carlen, 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 1477.35189 Carlen, Eric A.; Jauslin, Ian; Lieb, Elliott H. 2 2021 On the convolution inequality \(f\geq f\star f\). Zbl 1486.42006 Carlen, Eric A.; Jauslin, Ian; Lieb, Elliott H.; Loss, Michael P. 1 2021 The local density approximation in density functional theory. Zbl 1435.35320 Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2020 Divergence of the effective mass of a polaron in the strong coupling limit. Zbl 1446.81045 Lieb, Elliott H.; Seiringer, Robert 14 2020 Analysis of a simple equation for the ground state energy of the Bose gas. Zbl 1465.35345 Carlen, Eric A.; Jauslin, Ian; Lieb, Elliott H. 4 2020 Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 1479.46029 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 1 2020 Local incompressibility estimates for the Laughlin phase. Zbl 1410.82009 Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob 10 2019 Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062 Frank, Rupert L.; Lieb, Elliott H. 4 2019 Some trace inequalities for exponential and logarithmic functions. Zbl 1476.15034 Carlen, Eric A.; Lieb, Elliott H. 4 2019 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040 Frank, Rupert; Lieb, Elliott H. 17 2018 Statistical mechanics of the uniform electron gas. (Mécanique statistique pour le gaz uniforme d’électrons.) Zbl 1404.82003 Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 14 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 11 2018 Rigidity of the Laughlin liquid. Zbl 1398.81326 Lieb, Elliott H.; Rougerie, Nicolas; Yngvason, Jakob 8 2018 Nematic liquid crystal phase in a system of interacting dimers and monomers. Zbl 1400.82320 Jauslin, Ian; Lieb, Elliott H. 3 2018 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091 Frank, Rupert L.; Lieb, Elliott H. 7 2017 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023 Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 19 2016 Some operator and trace function convexity theorems. Zbl 1342.47024 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 13 2016 A Pfaffian formula for monomer-dimer partition functions. Zbl 1342.82161 Giuliani, Alessandro; Jauslin, Ian; Lieb, Elliott H. 6 2016 Entropy and entanglement bounds for reduced density matrices of fermionic states. Zbl 1342.81031 Carlen, Eric A.; Lieb, Elliott H.; Reuvers, Robin 5 2016 Proof of the Wehrl-type entropy conjecture for symmetric \({SU(N)}\) coherent states. Zbl 1365.81030 Lieb, Elliott H.; Solovej, Jan Philip 3 2016 On a quantum entropy power inequality of Audenaert, Datta, and Ozols. Zbl 1341.81015 Carlen, 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 1332.49042 Frank, Rupert L.; Lieb, Elliott H. 37 2015 Columnar phase in quantum dimer models. Zbl 1320.82011 Giuliani, Alessandro; Lieb, Elliott H. 2 2015 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 29 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 27 2014 Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. Zbl 1298.81116 Lieb, Elliott H.; Solovej, Jan Philip 19 2014 Remainder terms for some quantum entropy inequalities. Zbl 1292.81021 Carlen, Eric A.; Lieb, Elliott H. 16 2014 Equivalence of two definitions of the effective mass of a polaron. Zbl 1295.81055 Lieb, Elliott H.; Seiringer, Robert 9 2014 Formation of stripes and slabs near the ferromagnetic transition. Zbl 1302.82018 Giuliani, Alessandro; Lieb, Elliott H.; Seiringer, Robert 9 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075 Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Entropy meters and the entropy of non-extensive systems. Zbl 1371.80005 Lieb, Elliott H.; Yngvason, Jakob 4 2014 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099 Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 4 2014 Monotonicity of a relative Rényi entropy. Zbl 1350.94020 Frank, Rupert L.; Lieb, Elliott H. 79 2013 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 23 2013 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022 Frank, Rupert L.; Lieb, Elliott H. 10 2013 The entropy concept for non-equilibrium states. Zbl 1371.80004 Lieb, Elliott H.; Yngvason, Jakob 9 2013 Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures. Zbl 1270.26016 Carlen, Eric A.; Cordero-Erausquin, Dario; Lieb, Elliott H. 8 2013 Unique equilibria and substitution effects in a stochastic model of the marriage market. Zbl 1275.91098 Decker, Colin; Lieb, Elliott H.; McCann, Robert J.; Stephens, Benjamin K. 5 2013 On an extension problem for density matrices. Zbl 1282.81020 Carlen, Eric A.; Lebowitz, Joel L.; Lieb, Elliott H. 4 2013 A smooth complex generalization of the Hobby-Rice theorem. Zbl 1295.41025 Lazarev, Oleg; Lieb, Elliott H. 4 2013 Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 3 2013 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023 Frank, Rupert L.; Lieb, Elliott H. 106 2012 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023 Frank, Rupert L.; Lieb, Elliott H. 54 2012 Non-abelian vortices in supersymmetric gauge field theory via direct methods. Zbl 1255.81216 Lieb, Elliott H.; Yang, Yisong 17 2012 Bounds for entanglement via an extension of strong subadditivity of entropy. Zbl 1254.81019 Carlen, Eric A.; Lieb, Elliott H. 11 2012 Binding of polarons and atoms at threshold. Zbl 1250.82046 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Entropy and the uncertainty principle. Zbl 1256.81022 Frank, Rupert L.; Lieb, Elliott H. 6 2012 Further implications of the Bessis-Moussa-Villani conjecture. Zbl 1257.82009 Lieb, Elliott H.; Seiringer, Robert 1 2012 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 16 2011 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013 Frank, Rupert L.; Lieb, Elliott H. 7 2011 Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 3 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024 Frank, Rupert L.; Lieb, Elliott H. 65 2010 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 14 2010 Localization of multidimensional Wigner distributions. Zbl 1314.81129 Lieb, Elliott H.; Ostrover, Yaron 5 2010 The stability of matter in quantum mechanics. Zbl 1179.81004 Lieb, Elliott H.; Seiringer, Robert 107 2009 Probabilistic coherence and proper scoring rules. Zbl 1367.94139 Predd, Joel B.; Seiringer, Robert; Lieb, Elliott H.; Osherson, Daniel N.; Poor, H. Vincent; Kulkarni, Sanjeev R. 18 2009 Periodic minimizers in 1D local mean field theory. Zbl 1173.82008 Giuliani, Alessandro; Lebowitz, Joel L.; Lieb, Elliott H. 17 2009 Symmetry breaking in Laughlin’s state on a cylinder. Zbl 1155.81032 Jansen, S.; Lieb, E. H.; Seiler, R. 9 2009 Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices. Zbl 1190.15009 Carlen, Eric A.; Lieb, Elliott H. 4 2009 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 175 2008 A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity. Zbl 1171.47015 Carlen, Eric A.; Lieb, Elliott H. 41 2008 Brascamp–Lieb inequalities for non-commutative integration. Zbl 1173.46045 Carlen, Eric A.; Lieb, Elliott H. 3 2008 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 18 2007 Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 6 2007 Bose-Einstein condensation and spontaneous symmetry breaking. Zbl 1160.82308 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 5 2007 Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Zbl 1233.82004 Lieb, Elliott H.; Seiringer, Robert 98 2006 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382 Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 52 2006 An inequality of Hadamard type for permanents. Zbl 1116.15015 Carlen, Eric; Lieb, Elliott H.; Loss, Michael 18 2006 Bose-Einstein condensation as a quantum phase transition in an optical lattice. Zbl 1170.82325 Aizenman, M.; Lieb, E. H.; Seiringer, R.; Solovej, J. P.; Yngvason, J. 15 2006 Ground-state energy of a dilute Fermi gas. Zbl 1114.82004 Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip 4 2006 Ferromagnetism of the Hubbard model at strong coupling in the Hartree-Fock approximation. Zbl 1125.82031 Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V. 3 2006 Some matrix rearrangement inequalities. Zbl 1197.15011 Carlen, Eric; Lieb, Elliott H. 2 2006 The mathematics of the Bose gas and its condensation. Zbl 1104.82012 Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 227 2005 The stability of matter: From atoms to stars. Selecta of Elliott H. Lieb. 4th ed. Zbl 1165.01331 Lieb, Elliott H. 7 2005 The quantum-mechanical many-body problem: the Bose gas. Zbl 1113.82007 Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob 7 2005 Stronger subadditivity of entropy. Zbl 1227.82012 Lieb, Elliott H.; Seiringer, Robert 6 2005 One-dimensional behavior of dilute Bose gases in traps. Zbl 1106.82004 Seiringer, Robert; Lieb, Elliott H.; Yngvason, Jakob 5 2005 The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field. I: The lower bound. Zbl 1115.81064 Lieb, Elliott H.; Loss, Michael 5 2005 A sharp analog of Young’s inequality on \(S^N\) and related entropy inequalities. Zbl 1056.43002 Carlen, E. A.; Lieb, E. H.; Loss, M. 55 2004 Ground state energy of the two-component charged Bose gas. Zbl 1124.82303 Lieb, Elliott H.; Solovej, Jan Philip 33 2004 Equivalent forms of the Bessis-Moussa-Villani conjecture. Zbl 1157.81313 Lieb, Elliott H.; Seiringer, Robert 23 2004 One-dimensional behavior of dilute, trapped Bose gases. Zbl 1075.82002 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 20 2004 A note on polarization vectors in quantum electrodynamics. Zbl 1102.81070 Lieb, Elliott H.; Loss, Michael 17 2004 Quantum mechanics, the stability of matter and quantum electrodynamics. Zbl 1255.81002 Lieb, Elliott H. 3 2004 Condensed matter physics and exactly soluble models. Selecta of Elliott H. Lieb. Edited by B. Nachtergaele, J. P. Solovej and J. Yngvason. Zbl 1113.01026 Lieb, Elliott H. 3 2004 The stability of matter and quantum electrodynamics. Zbl 1081.81566 Lieb, Elliott H. 2 2004 A short appreciation of Freeman Dyson’s long career in mathematical physics. Zbl 1101.01315 Lieb, Elliott 1 2004 Existence of atoms and molecules in non-relativistic quantum electrodynamics. Zbl 1058.81080 Lieb, Elliott H.; Loss, Michael 37 2003 Bose-Einstein condensation of dilute gases in traps. Zbl 1041.81107 Lieb, Elliott H.; Seiringer, Robert 28 2003 Poincaré inequalities in punctured domains. Zbl 1048.26012 Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob 16 2003 The one-dimensional Hubbard model: a reminiscence. Zbl 1037.82009 Lieb, Elliott H.; Wu, F. Y. 15 2003 The entropy of classical thermodynamics. Zbl 1163.80300 Lieb, Elliott H.; Yngvason, Jakob 2 2003 Ground state energy of the one-component charged Bose gas. Zbl 1042.82004 Lieb, Elliott H.; Solovej, Jan Philip 41 2002 A bound on binding energies and mass renormalization in models of quantum electrodynamics. Zbl 1027.81040 Lieb, Elliott H.; Loss, Michael 19 2002 Stability of a model of relativistic quantum electrodynamics. Zbl 1005.81091 Lieb, Elliott H.; Loss, Michael 11 2002 ...and 127 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,809 Authors 112 Lieb, Elliott Hershel 91 Frank, Rupert L. 81 Seiringer, Robert 55 Solovej, Jan Philip 55 Tang, Xianhua 53 Lewin, Mathieu 52 Yang, Minbo 48 Rădulescu, Vicenţiu D. 45 Schlein, Benjamin 45 Tang, Chun-Lei 42 Chen, Haibo 41 Carlen, Eric Anders 41 Wu, Tsungfang 39 Loss, Michael 38 Fröhlich, Jürg Martin 37 Ambrosio, Vincenzo 37 Laptev, Ari 36 Alves, Claudianor Oliveira 36 Dolbeault, Jean 36 Phan Thành Nam 35 Chen, Sitong 34 Rougerie, Nicolas 34 Zou, Wenming 31 Hainzl, Christian 31 Peng, Shuangjie 30 Deng, Yinbin 30 Squassina, Marco 30 Van Schaftingen, Jean 29 Siedentop, Heinz Karl Heinrich 28 Miyagaki, Olimpio Hiroshi 26 Lu, Guozhen 25 Brézis, Haïm 25 Fournais, Søren 25 Lei, Yutian 24 Erdős, László 24 He, Xiaoming 24 Simon, Barry 24 Sreenadh, Konijeti 24 Zhang, Binlin 23 Guo, Yujin 23 Sun, Juntao 22 Figueiredo, Giovany Malcher 22 Salani, Paolo 21 Bach, Volker 21 Chen, Jianqing 21 Lei, Chunyu 21 Liang, Sihua 21 Lions, Pierre-Louis 21 Pucci, Patrizia 21 Wang, Jun 20 Carrillo de la Plata, José Antonio 20 Naor, Assaf 20 Ruskai, Mary Beth 19 Cao, Daomin 19 Chen, Thomas 19 Fiscella, Alessio 19 Hiai, Fumio 19 Nachtergaele, Bruno 19 Petz, Dénes 19 Ruzhansky, Michael V. 19 Wang, Zhi-Qiang 19 Xiao, Jie 19 Yau, Horng-Tzer 19 Yngvason, Jakob 18 Benguria, Rafael D. 18 Gao, Fashun 18 Hajaiej, Hichem 18 Hiroshima, Fumio 18 Liao, Jiafeng 18 Miyao, Tadahiro 18 Sigal, Israel Michael 18 Suragan, Durvudkhan 18 Xue, Kang 18 Yang, Jianfu 17 Hansen, Frank-Peter 17 Hsu, TsingSan 17 Liu, Zhisu 17 Nguyễn Văn Hoàng 17 Repovš, Dušan D. 17 Spohn, Herbert 16 Esteban, Maria J. 16 Faupin, Jérémy 16 Griesemer, Marcel 16 Ilyin, Aleksei A. 16 Li, Congming 16 Li, Guidong 16 Lü, Dengfeng 16 Serfaty, Sylvia 16 Su, Jiabao 16 Vugal’ter, Semën Abramovich 15 Bez, Neal 15 Cingolani, Silvia 15 Csikvári, Péter 15 Dou, Jingbo 15 Feng, Binhua 15 Jeanjean, Louis 15 Li, Gongbao 15 Saanouni, Tarek 15 Slavnov, Nikita A. 15 Tasaki, Hal ...and 7,709 more Authors all top 5 Cited in 644 Serials 454 Journal of Mathematical Physics 413 Communications in Mathematical Physics 311 Journal of Functional Analysis 310 Journal of Mathematical Analysis and Applications 254 Journal of Differential Equations 253 Nonlinear Analysis. 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