Edit Profile (opens in new tab) Milman, Vitali D. Compute Distance To: Compute Author ID: milman.vitali-d Published as: Milman, V. D.; Milman, Vitali; Mil’man, V. D.; Milman, V.; Milman, Vitali D.; Mil’man, Vitali D. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 215 Publications since 1960, including 5 Books 20 Contributions as Editor · 2 Further Contributions Co-Authors: 71 Co-Authors with 182 Joint Publications 2,457 Co-Co-Authors all top 5 Co-Authors 54 single-authored 27 Artstein-Avidan, Shiri 20 König, Hermann 18 Bourgain, Jean 13 Lindenstrauss, Joram 13 Tomczak-Jaegermann, Nicole 12 Giannopoulos, Apostolos A. 11 Schechtman, Gideon 10 Alon, Noga 10 Pajor, Alain 10 Rotem, Liran 9 Klartag, Bo’az 9 Litvak, Aleksandr Evgen’evich 8 Gromov, Mikhael Leonidovich 6 Szarek, Stanislaw Jerzy 5 Mil’man, D. P. 4 Alesker, Semyon 4 Connes, Alain 4 Faifman, Dmitry 4 Florentin, Dan Itzhak 4 Karpovsky, Mark G. 4 Pisier, Gilles 3 Figiel, Tadeusz 3 Friedland, Omer 3 Gluskin, Efim D. 3 Myshkis, Anatoliĭ Dmitrievich 3 Segal, Alexander 3 Wolfson, Haim J. 2 Amir, Dan 2 Ball, Keith Martin 2 Kononenko, A. I. 2 Lindenstrauss, Elon 2 Schneider, Rolf G. 2 Sharir, Micha 2 Tsolomitis, Antonis 2 Wagner, Roy 1 Aron, Richard Martin 1 Ben-Efraim, Limor 1 Benyamini, Yoav 1 Curbera, Guillermo P. 1 Daubechies, Ingrid Chantal 1 Davis, William Jay 1 Delbaen, Freddy 1 Deza, Michel Marie 1 Dineen, Seán 1 Eidelman, Yuli 1 Eliashberg, Yakov Matveevich 1 Enflo, Per Henrik 1 Galil, Zvi 1 Ghoussoub, Nassif A. 1 Guth, Lawrence David 1 Jitomirskaya, Svetlana Yakovlevna 1 Johnson, William Buhmann 1 Kadets, Mikhail I. 1 Kontorovich, Alex V. 1 Lev, A. Ju. 1 Lindenstrauss, Ayelet 1 Ludwig, Monika 1 Lyubich, Yuriĭ Il’ich 1 Maurey, Bernard 1 Mendelson, Shahar 1 Meyer, Mathieu 1 Milman, Emanuel 1 Milman, Pierre D. 1 Naor, Assaf 1 Ostrover, Yaron 1 Ostrovskiĭ, Iosif Vladimirovich 1 Perelson, Alan S. 1 Pestov, Vladimir G. 1 Polterovich, Leonid Viktorovich 1 Preiss, David 1 Rudelson, Mark 1 Rudnick, Zeév 1 Sarnak, Peter Clive 1 Schlag, Wilhelm 1 Schoen, Richard Melvin 1 Slomka, Boaz A. 1 Sodin, Mikhail 1 Sodin, Sasha 1 Staffilani, Gigliola 1 Szankowski, Andrzej 1 Tao, Terence 1 Tkachenko, Vadim Aleksandrovich 1 Tumarkin, Yu. B. 1 Varjú, Péter Pál 1 Zalcman, Lawrence Allen all top 5 Serials 12 Israel Journal of Mathematics 12 Journal of Functional Analysis 12 Soviet Mathematics. Doklady 10 Lecture Notes in Mathematics 9 Comptes Rendus de l’Académie des Sciences. Série I 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Proceedings of the American Mathematical Society 4 Teoriya Funktsiĭ, Funktsional’nyĭ Analiz i ikh Prilozheniya 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Electronic Research Announcements in Mathematical Sciences 3 Discrete Mathematics 3 Russian Mathematical Surveys 3 Studia Mathematica 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Advances in Mathematics 3 Functional Analysis and its Applications 3 Matematicheskiĭ Sbornik. Novaya Seriya 3 Notices of the American Mathematical Society 3 St. Petersburg Mathematical Journal 3 Journal of Mathematical Physics, Analysis, Geometry 2 Acta Mathematica 2 Geometriae Dedicata 2 Inventiones Mathematicae 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Geometric and Functional Analysis. GAFA 2 Annals of Mathematics. Second Series 2 Advances in Geometry 2 Mathematical Sciences Research Institute Publications 2 Mathematical Surveys and Monographs 2 Proceedings of the Steklov Institute of Mathematics 2 Modern Birkhäuser Classics 1 Doklady Akademii Nauk SSSR 1 American Journal of Mathematics 1 The Annals of Probability 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Illinois Journal of Mathematics 1 Integral Equations and Operator Theory 1 Journal of Combinatorial Theory. Series B 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematika 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Journal of Algorithms 1 IMRN. International Mathematics Research Notices 1 Problemy Peredachi Informatsii 1 Zagadnienia Drgań Nieliniowych 1 Combinatorics, Probability and Computing 1 Documenta Mathematica 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Milan Journal of Mathematics 1 Bulletin of the American Mathematical Society 1 Revue du CETHEDEC 1 Fields Institute Communications 1 Graduate Studies in Mathematics 1 Israel Mathematical Conference Proceedings 1 Translations. Series 2. American Mathematical Society 1 Operator Theory: Advances and Applications all top 5 Fields 115 Functional analysis (46-XX) 101 Convex and discrete geometry (52-XX) 29 Real functions (26-XX) 21 Operator theory (47-XX) 20 General and overarching topics; collections (00-XX) 18 Difference and functional equations (39-XX) 14 Probability theory and stochastic processes (60-XX) 11 History and biography (01-XX) 7 Combinatorics (05-XX) 5 Measure and integration (28-XX) 5 Differential geometry (53-XX) 4 Number theory (11-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 General topology (54-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Abstract harmonic analysis (43-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Algebraic topology (55-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 174 Publications have been cited 2,996 times in 1,864 Documents Cited by ▼ Year ▼ Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds. Zbl 0606.46013Milman, Vitali D.; Schechtman, Gideon 260 1986 \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators. Zbl 0549.05051Alon, N.; Milman, V. D. 257 1985 The dimension of almost spherical sections of convex bodies. Zbl 0375.52002Figiel, T.; Lindenstrauss, J.; Milman, V. D. 152 1977 Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed \(n\)-dimensional space. Zbl 0679.46012Milman, V. D.; Pajor, A. 147 1989 New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006Bourgain, J.; Milman, V. D. 142 1987 A topological application of the isoperimetric inequality. Zbl 0522.53039Gromov, Mikhael; Milman, V. D. 142 1983 Global versus local asymptotic theories of finite-dimensional normed spaces. Zbl 0911.52002Milman, V. D.; Schechtman, G. 121 1997 Asymptotic geometric analysis. I. Zbl 1337.52001Artstein-Avidan, Shiri; Giannopoulos, Apostolos; Milman, Vitali D. 107 2015 On the stability of motion in the presence of impulses. Zbl 1358.34022Mil’man, V. D.; Myškis, A. D. 101 1960 The Santaló point of a function, and a functional form of the Santaló inequality. Zbl 1121.52021Artstein-Avidan, S.; Klartag, B.; Milman, V. 75 2004 Approximation of zonoids by zonotopes. Zbl 0682.46008Bourgain, J.; Lindenstrauss, J.; Milman, V. 69 1989 Geometry of log-concave functions and measures. Zbl 1099.28002Klartag, B.; Milman, V. D. 62 2005 Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces. Zbl 0623.46007Gromov, M.; Milman, V. D. 58 1987 Extremal problems and isotropic positions of convex bodies. Zbl 0964.52004Giannopoulos, A. A.; Milman, V. D. 49 2000 The concept of duality in convex analysis, and the characterization of the Legendre transform. Zbl 1173.26008Artstein-Avidan, Shiri; Milman, Vitali 45 2009 Entropy and asymptotic geometry of non-symmetric convex bodies. Zbl 0974.52004Milman, V. D.; Pajor, A. 41 2000 Asymptotic infinite-dimensional theory of Banach spaces. Zbl 0872.46013Maurey, B.; Milman, V. D.; Tomczak-Jaegermann, N. 36 1995 On type of metric spaces. Zbl 0617.46024Bourgain, J.; Milman, V.; Wolfson, H. 35 1986 Averages of norms and quasi-norms. Zbl 0920.46006Litvak, A. E.; Milman, V. D.; Schechtman, G. 33 1998 Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés. (An inverse form of the Brunn-Minkowski inequality with applications to local theory of normed spaces). Zbl 0604.52003Milman, Vitali D. 31 1986 Euclidean structure in finite dimensional normed spaces. Zbl 1009.46004Giannopoulos, Apostolos A.; Milman, Vitali D. 31 2001 The local theory of normed spaces and its applications to convexity. Zbl 0791.52003Lindenstrauss, J.; Milman, V. D. 26 1993 The concept of duality for measure projections of convex bodies. Zbl 1145.26003Artstein-Avidan, Shiri; Milman, Vitali 26 2008 Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space. Zbl 0581.46014Milman, V. D. 23 1985 Unconditional and symmetric sets in \(n\)-dimensional normed spaces. Zbl 0445.46011Amir, D.; Milman, V. D. 23 1980 Some properties of strictly singular operators. Zbl 0179.17801Mil’man, V. D. 22 1969 Coordinate density of sets of vectors. Zbl 0401.05015Karpovsky, M. G.; Milman, V. D. 21 1978 Better expanders and superconcentrators. Zbl 0641.68102Alon, N.; Galil, Z.; Milman, V. D. 21 1987 Geometric theory of Banach spaces. Part I: The theory of basis and minimal systems. Zbl 0221.46015Mil’man, V. D. 21 1970 Hidden structures in the class of convex functions and a new duality transform. Zbl 1221.26018Artstein-Avidan, Shiri; Milman, Vitali 21 2011 Asymptotic \(\ell_ p\) spaces and bounded distortions. Zbl 0822.46007Milman, Vitali D.; Tomczak-Jaegermann, Nicole 20 1993 Mixed integrals and related inequalities. Zbl 1267.26021Milman, Vitali; Rotem, Liran 19 2013 Concentration property on probability spaces. Zbl 1068.28002Giannopoulos, A. A.; Milman, V. D. 19 2000 Duality of metric entropy. Zbl 1072.52001Artstein, S.; Milman, V.; Szarek, S. J. 19 2004 Banach spaces with a weak cotype 2 property. Zbl 0611.46022Milman, Vitali D.; Pisier, Gilles 18 1986 Minkowski sums and symmetrizations. Zbl 0645.52001Bourgain, J.; Lindenstrauss, J.; Milman, V. D. 18 1988 Functional analysis. An introduction. Zbl 1077.46001Eidelman, Yuli; Milman, Vitali; Tsolomitis, Antonis 18 2004 A characterization of the concept of duality. Zbl 1140.52300Artstein-Avidan, Shiri; Milman, Vitali 17 2008 Symmetrization and isotropic constants of convex bodies. Zbl 1070.52002Bourgain, J.; Klartag, B.; Milman, V. 17 2004 Embedding of \(\ell^ k_{\infty}\) in finite dimensional Banach spaces. Zbl 0546.46015Alon, N.; Milman, V. D. 16 1983 Asymptotic formulas for the diameter of sections of symmetric convex bodies. Zbl 1088.46006Giannopoulos, Apostolos; Milman, Vitali D.; Tsolomitis, Antonis 16 2005 Geometrization of probability. Zbl 1154.60022Milman, Vitali D. 15 2008 Convex bodies with minimal mean width. Zbl 0978.52001Giannopoulos, A. A.; Milman, V. D.; Rudelson, M. 14 2000 A remarkable measure preserving diffeomorphism between two convex bodies in \(\mathbb{R}^n\). Zbl 0927.52007Alesker, S.; Dar, S.; Milman, V. 14 1999 A characterization of the support map. Zbl 1192.52004Artstein-Avidan, S.; Milman, V. 13 2010 The heritage of P. Lévy in geometrical functional analysis. Zbl 0681.46021Milman, V. D. 12 1988 On Hilbertian subsets of finite metric spaces. Zbl 0634.46008Bourgain, J.; Figiel, T.; Milman, V. 12 1986 Gaussian processes and mixed volumes. Zbl 0636.60036Milman, V. D.; Pisier, G. 12 1987 Mean width and diameter of proportional sections of a symmetric convex body. Zbl 0896.52007Giannopoulos, A. A.; Milman, V. D. 12 1998 The M-ellipsoid, symplectic capacities and volume. Zbl 1138.53060Artstein-Avidan, Shiri; Milman, Vitali; Ostrover, Yaron 12 2008 On the diameter of proportional sections of a symmetric convex body. Zbl 0877.52009Giannopoulos, A. A.; Milman, V. D. 11 1997 Some applications of duality relations. Zbl 0818.46016Milman, V. 10 1991 Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality. Zbl 0588.46013Milman, V. D. 10 1985 Estimates related to Steiner symmetrizations. Zbl 0673.52001Bourgain, J.; Lindenstrauss, J.; Milman, V. 10 1989 Geometric theory of Banach spaces. II: Geometry of the unit sphere. Zbl 0238.46012Mil’man, V. D. 10 1972 New proof of the theorem of A. Dvoretzky on intersections of convex bodies. Zbl 0239.46018Mil’man, V. D. 10 1972 Sections euclidiennes et volume des corps symétriques convexes dans \(R^ n\). (Euclidean sections and volume of symmetric convex bodies in \(R^ n.)\). Zbl 0576.52002Bourgain, Jean; Milman, Vitali D. 9 1985 A characterization of product preserving maps with applications to a characterization of the Fourier transform. Zbl 1272.42004Alesker, S.; Artstein-Avidan, S.; Faifman, D.; Milman, V. 9 2010 The chain rule as a functional equation. Zbl 1203.39014Artstein-Avidan, Shiri; König, Hermann; Milman, Vitali 9 2010 Rapid Steiner symmetrization of most of a convex body and the slicing problem. Zbl 1084.52003Klartag, B.; Milman, V. 9 2005 The covering numbers and “low \(M^*\)-estimate” for quasi-convex bodies. Zbl 0948.52005Litvak, A. E.; Milman, V. D.; Pajor, A. 9 1999 Regularization of star bodies by random hyperplane cut off. Zbl 1076.46008Milman, V. D.; Pajor, A. 9 2003 Characterizing the derivative and the entropy function by the Leibniz rule. Zbl 1231.39011König, Hermann; Milman, Vitali 9 2011 Geometric probability and random cotype 2. Zbl 1087.46006Gluskin, E.; Milman, V. 9 2004 Brunn theorem and a concentration of volume phenomena for symmetric convex bodies. Zbl 0953.52500Gromov, M.; Milman, V. D. 8 1984 Geometric applications of Chernoff-type estimates and a zigzag approximation for balls. Zbl 1119.46012Artstein-Avidan, S.; Friedland, O.; Milman, V. 8 2006 Die geometrische Theorie der Banachräume. II: Die Geometrie der Einheitssphäre. (Geometric theory of Banach spaces. II: Geometry of the unit sphere). Zbl 0229.46017Mil’man, V. D. 8 1971 On a geometric inequality. Zbl 0653.46015Bourgain, J.; Meyer, M.; Milman, V.; Pajor, A. 8 1988 Topics in asymptotic geometric analysis. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.46010Milman, V. 8 2000 Isomorphic Steiner symmetrization. Zbl 1034.52008Klartag, B.; Milman, V. D. 7 2003 Non-standard constructions in convex geometry: geometric means of convex bodies with an appendix by Alexander Magazinov. (Non-standard constructions in convex geometry: geometric means of convex bodies.) Zbl 1381.52006Milman, Vitali; Rotem, Liran 7 2017 An “isomorphic” version of Dvoretzky’s theorem. Zbl 0836.46007Milman, Vitali D.; Schechtman, Gideon 7 1995 Infinite-dimensional geometry of the unit sphere in Banach space. Zbl 0175.13201Mil’man, V. D. 7 1967 An “isomorphic” version of Dvoretzky’s theorem. II. Zbl 0942.46012Milman, Vitali; Schechtman, Gideon 7 1999 A note on a low \(M^*\)-estimate. Zbl 0760.46009Milman, V. 6 1991 Geometrical inequalities and mixed volumes in the local theory of Banach spaces. Zbl 0582.46015Milman, V. D. 6 1985 Dichotomie du cotype pour les espaces invariants. (Dichotomy of cotype for invariant spaces). Zbl 0584.43005Bourgain, Jean; Milman, Vitali 6 1985 A new proof of the Maurey-Pisier theorem. Zbl 0418.46010Milman, V. D.; Sharir, M. 6 1979 Order isomorphisms on convex functions in windows. Zbl 1266.26021Artstein-Avidan, Shiri; Florentin, Dan; Milman, Vitali 6 2012 Asymptotic properties of functions of several variables defined on homogeneous spaces. Zbl 0236.26009Mil’man, V. D. 6 1971 The geometry of nested families with empty intersection. Structure of the unit sphere of a nonreflexive space. Zbl 0196.13501Mil’man, D. P.; Mil’man, V. D. 6 1969 Spectrum of bounded continuous functions specified on a unit sphere in Banach space. Zbl 0203.45001Mil’man, V. D. 6 1969 Polynomial bounds for large Bernoulli sections of \(\ell_1^N\). Zbl 1160.60004Artstein-Avidan, Shiri; Friedland, Omer; Milman, Vitali; Sodin, Sasha 6 2006 On convexified packing and entropy duality. Zbl 1062.52023Artstein, S.; Milman, V.; Szarek, S.; Tomczak-Jaegermann, N. 6 2004 Minkowski spaces with extremal distance from the Euclidean space. Zbl 0374.46013Milman, V. D.; Wolfson, H. 6 1978 Asymptotic convex geometry – short overview. Zbl 1068.52011Giannopoulos, A. A.; Milman, V. D. 6 2004 Shrinking minimal systems and complementation of \(\ell^n_p\)-spaces in reflexive Banach spaces. Zbl 0418.46009Milman, V. D.; Sharir, M. 5 1979 A quantitative finite-dimensional Krivine theorem. Zbl 0612.46021Amir, D.; Milman, V. D. 5 1985 Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. Zbl 1111.52009Artstein-Avidan, S.; Milman, V. D. 5 2006 \(\alpha\)-concave functions and a functional extension of mixed volumes. Zbl 1277.52011Milman, Vitali; Rotem, Liran 5 2013 The distance between certain \(n\)-dimensional Banach spaces. Zbl 0475.46010Davis, W. J.; Milman, V. D.; Tomczak-Jaegermann, Nicole 5 1981 Isomorphic symmetrization and geometric inequalities. Zbl 0652.52008Milman, V. D. 5 1988 A geometric lemma and duality of entropy numbers. Zbl 0987.46017Milman, V. D.; Szarek, S. J. 5 2000 How small can the intersection of a few rotations of a symmetric convex body be? Zbl 0889.52003Giannopoulos, Apostolos A.; Milman, Vitali D. 5 1997 Dvoretzky’s theorem – thirty years later. Zbl 0787.46016Milman, V. 5 1992 Random shocks in linear dynamical systems. Zbl 0133.10403Mil’man, V. D.; Myshkis, A. D. 5 1963 Weighted geometric means of convex bodies. Zbl 1430.52003Milman, Vitali; Rotem, Liran 4 2019 Rigidity and stability of the Leibniz and the chain rule. Zbl 1301.39016König, Hermann; Milman, Vitali 4 2013 Characterizing addition of convex sets by polynomiality of volume and by the homothety operation. Zbl 1316.52004Milman, Vitali; Rotem, Liran 4 2015 Note on the geometric-arithmetic mean inequality. Zbl 1035.26020Gluskin, E.; Milman, V. 4 2003 The slicing problem by Bourgain. Zbl 07672489Klartag, B.; Milman, V. 1 2022 Reciprocals and flowers in convexity. Zbl 1460.52007Milman, Emanuel; Milman, Vitali; Rotem, Liran 2 2020 Novel view on classical convexity theory. Zbl 1488.52006Milman, Vitali; Rotem, Liran 1 2020 Weighted geometric means of convex bodies. Zbl 1430.52003Milman, Vitali; Rotem, Liran 4 2019 “Irrational” constructions in convex geometry. Zbl 1394.52004Milman, V.; Rotem, L. 2 2018 Tribute to Joe Diestel (1943–2017). Zbl 1398.01023Aron, Richard; Dineen, Seán; Milman, Vitali; Enflo, Per; Curbera, Guillermo P. 1 2018 Operator relations characterizing derivatives. Zbl 1478.47001König, Hermann; Milman, Vitali 1 2018 Non-standard constructions in convex geometry: geometric means of convex bodies with an appendix by Alexander Magazinov. (Non-standard constructions in convex geometry: geometric means of convex bodies.) Zbl 1381.52006Milman, Vitali; Rotem, Liran 7 2017 Powers and logarithms of convex bodies. (Puissances et logarithmes de corps convexes.) Zbl 1380.52008Milman, Vitali; Rotem, Liran 4 2017 A characterization of the mixed discriminant. Zbl 1341.15004Florentin, D.; Milman, V. D.; Schneider, R. 2 2016 Asymptotic geometric analysis. I. Zbl 1337.52001Artstein-Avidan, Shiri; Giannopoulos, Apostolos; Milman, Vitali D. 107 2015 Characterizing addition of convex sets by polynomiality of volume and by the homothety operation. Zbl 1316.52004Milman, Vitali; Rotem, Liran 4 2015 On the oscillation rigidity of a Lipschitz function on a high-dimensional flat torus. Zbl 1323.46010Faifman, Dmitry; Klartag, Bo’az; Milman, Vitali 2 2014 Submultiplicative functions and operator inequalities. Zbl 1317.39034König, Hermann; Milman, Vitali 2 2014 The derivation equation for \(C^k\)-functions: stability and localization. Zbl 1308.39019König, Hermann; Milman, Vitali 1 2014 Mixed integrals and related inequalities. Zbl 1267.26021Milman, Vitali; Rotem, Liran 19 2013 \(\alpha\)-concave functions and a functional extension of mixed volumes. Zbl 1277.52011Milman, Vitali; Rotem, Liran 5 2013 Rigidity and stability of the Leibniz and the chain rule. Zbl 1301.39016König, Hermann; Milman, Vitali 4 2013 Operator functional equations in analysis. Zbl 1266.39024König, Hermann; Milman, Vitali 2 2013 Asymptotic geometric analysis. Proceedings of the fall 2010 Fields Institute thematic program. Zbl 1262.00011 1 2013 Stability results for some classical convexity operations. Zbl 1268.52007Artstein-Avidan, Shiri; Milman, Vitali 1 2013 An operator equation characterizing the Laplacian. Zbl 1273.47035König, H.; Milman, V. 1 2013 Order isomorphisms on convex functions in windows. Zbl 1266.26021Artstein-Avidan, Shiri; Florentin, Dan; Milman, Vitali 6 2012 An operator equation generalizing the Leibniz rule for the second derivative. Zbl 1262.39031König, Hermann; Milman, Vitali 4 2012 On multiplicative maps of continuous and smooth functions. Zbl 1267.39016Artstein-Avidan, Shiri; Faifman, Dmitry; Milman, Vitali 3 2012 Hidden structures in the class of convex functions and a new duality transform. Zbl 1221.26018Artstein-Avidan, Shiri; Milman, Vitali 21 2011 Characterizing the derivative and the entropy function by the Leibniz rule. Zbl 1231.39011König, Hermann; Milman, Vitali 9 2011 A characterization of duality through section/projection correspondence in the finite dimensional setting. Zbl 1258.52002Milman, Vitali D.; Segal, Alexander; Slomka, Boaz A. 4 2011 Order isomorphisms in windows. Zbl 1225.26023Artstein-Avidan, Shiri; Florentin, Dan; Milman, Vitali 3 2011 Characterizing the mixed volume. Zbl 1242.52011Milman, Vitali D.; Schneider, Rolf 3 2011 A functional equation characterizing the second derivative. Zbl 1226.39009König, Hermann; Milman, Vitali 1 2011 A characterization of the support map. Zbl 1192.52004Artstein-Avidan, S.; Milman, V. 13 2010 A characterization of product preserving maps with applications to a characterization of the Fourier transform. Zbl 1272.42004Alesker, S.; Artstein-Avidan, S.; Faifman, D.; Milman, V. 9 2010 The chain rule as a functional equation. Zbl 1203.39014Artstein-Avidan, Shiri; König, Hermann; Milman, Vitali 9 2010 Essentially-Euclidean convex bodies. Zbl 1200.46019Litvak, Alexander E.; Milman, Vitali D.; Tomczak-Jaegermann, Nicole 2 2010 Visions in mathematics. GAFA 2000 special volume, Part II. Proceedings of the meeting “Visions in Mathematics – Towards 2000, Tel Aviv, Israel, August 25–September 3, 1999. Special volume of the journal Geometric and Functional Analysis – GAFA. Reprint of the 2000 original. Zbl 1185.00038 1 2010 The concept of duality in convex analysis, and the characterization of the Legendre transform. Zbl 1173.26008Artstein-Avidan, Shiri; Milman, Vitali 45 2009 A characterization of the Fourier transform and related topics. Zbl 1184.42009Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali 4 2009 The concept of duality for measure projections of convex bodies. Zbl 1145.26003Artstein-Avidan, Shiri; Milman, Vitali 26 2008 A characterization of the concept of duality. Zbl 1140.52300Artstein-Avidan, Shiri; Milman, Vitali 17 2008 Geometrization of probability. Zbl 1154.60022Milman, Vitali D. 15 2008 The M-ellipsoid, symplectic capacities and volume. Zbl 1138.53060Artstein-Avidan, Shiri; Milman, Vitali; Ostrover, Yaron 12 2008 A characterization of the Fourier transform and related topics. Zbl 1283.42008Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali 3 2008 A new duality transform. Zbl 1171.26007Artstein-Avidan, Shiri; Milman, Vitali 1 2008 Using Rademacher permutations to reduce randomness. Zbl 1131.60004Artstein-Avidan, S.; Milman, V. D. 1 2008 Geometric applications of Chernoff-type estimates. Zbl 1146.46004Artstein-Avidan, S.; Friedland, O.; Milman, V. 4 2007 On the Euclidean metric entropy of convex bodies. Zbl 1132.52006Litvak, A. E.; Milman, V. D.; Pajor, A.; Tomczak-Jaegermann, N. 3 2007 Geometric applications of Chernoff-type estimates and a zigzag approximation for balls. Zbl 1119.46012Artstein-Avidan, S.; Friedland, O.; Milman, V. 8 2006 Polynomial bounds for large Bernoulli sections of \(\ell_1^N\). Zbl 1160.60004Artstein-Avidan, Shiri; Friedland, Omer; Milman, Vitali; Sodin, Sasha 6 2006 Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. Zbl 1111.52009Artstein-Avidan, S.; Milman, V. D. 5 2006 Entropy extension. Zbl 1118.52014Litvak, A. E.; Milman, V. D.; Pajor, A.; Tomczak-Jaegermann, N. 1 2006 Geometry of log-concave functions and measures. Zbl 1099.28002Klartag, B.; Milman, V. D. 62 2005 Asymptotic formulas for the diameter of sections of symmetric convex bodies. Zbl 1088.46006Giannopoulos, Apostolos; Milman, Vitali D.; Tsolomitis, Antonis 16 2005 Rapid Steiner symmetrization of most of a convex body and the slicing problem. Zbl 1084.52003Klartag, B.; Milman, V. 9 2005 The Santaló point of a function, and a functional form of the Santaló inequality. Zbl 1121.52021Artstein-Avidan, S.; Klartag, B.; Milman, V. 75 2004 Duality of metric entropy. Zbl 1072.52001Artstein, S.; Milman, V.; Szarek, S. J. 19 2004 Functional analysis. An introduction. Zbl 1077.46001Eidelman, Yuli; Milman, Vitali; Tsolomitis, Antonis 18 2004 Symmetrization and isotropic constants of convex bodies. Zbl 1070.52002Bourgain, J.; Klartag, B.; Milman, V. 17 2004 Geometric probability and random cotype 2. Zbl 1087.46006Gluskin, E.; Milman, V. 9 2004 On convexified packing and entropy duality. Zbl 1062.52023Artstein, S.; Milman, V.; Szarek, S.; Tomczak-Jaegermann, N. 6 2004 Asymptotic convex geometry – short overview. Zbl 1068.52011Giannopoulos, A. A.; Milman, V. D. 6 2004 Isomorphic random subspaces and quotients of convex and quasi-convex bodies. Zbl 1071.52007Litvak, A. E.; Milman, V. D.; Tomczak-Jaegermann, N. 1 2004 Essential uniqueness of an M-ellipsoid of a given convex body. Zbl 1067.52005Milman, V. D.; Pajor, A. 1 2004 Regularization of star bodies by random hyperplane cut off. Zbl 1076.46008Milman, V. D.; Pajor, A. 9 2003 Isomorphic Steiner symmetrization. Zbl 1034.52008Klartag, B.; Milman, V. D. 7 2003 Note on the geometric-arithmetic mean inequality. Zbl 1035.26020Gluskin, E.; Milman, V. 4 2003 A reduction of the slicing problem to finite volume ratio bodies. Zbl 1036.52005Bourgain, Jean; Klartag, Bo’az; Milman, Vitali 4 2003 Some remarks on a lemma of Ran Raz. Zbl 1070.46009Milman, Vitali; Wagner, Roy 2 2003 Duality of metric entropy in Euclidean space. Zbl 1042.52002Artstein, Shiri; Milman, Vitali D.; Szarek, Stanislaw J. 2 2003 More on the duality conjecture for entropy numbers. Zbl 1042.52001Artstein, Shiri; Milman, Vitali D.; Szarek, Stanislaw J. 1 2003 Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 2001–2002. Zbl 1009.00019 1 2003 Randomizing properties of convex high-dimensional bodies and some geometric inequalities. Zbl 1019.46009Gluskin, Efim; Milman, Vitali 2 2002 Euclidean structure in finite dimensional normed spaces. Zbl 1009.46004Giannopoulos, Apostolos A.; Milman, Vitali D. 31 2001 A geometric approach to duality of metric entropy. Zbl 0983.46013Milman, Vitali D.; Szarek, Stanislaw J. 1 2001 Extremal problems and isotropic positions of convex bodies. Zbl 0964.52004Giannopoulos, A. A.; Milman, V. D. 49 2000 Entropy and asymptotic geometry of non-symmetric convex bodies. Zbl 0974.52004Milman, V. D.; Pajor, A. 41 2000 Concentration property on probability spaces. Zbl 1068.28002Giannopoulos, A. A.; Milman, V. D. 19 2000 Convex bodies with minimal mean width. Zbl 0978.52001Giannopoulos, A. A.; Milman, V. D.; Rudelson, M. 14 2000 Topics in asymptotic geometric analysis. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.46010Milman, V. 8 2000 A geometric lemma and duality of entropy numbers. Zbl 0987.46017Milman, V. D.; Szarek, S. J. 5 2000 GAFA 2000. Visions in mathematics—Towards 2000. Proceedings of a meeting, Tel Aviv, Israel, August 25–September 3, 1999. Part II. Special volume of the journal Geometric and Functional Analysis. Zbl 0960.00035 1 2000 Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 1996–2000. Zbl 0949.00025 1 2000 Stabilized asymptotic structures and envelopes in Banach spaces. Zbl 0987.46025Milman, V. D.; Tomczak-Jaegermann, N. 1 2000 A remarkable measure preserving diffeomorphism between two convex bodies in \(\mathbb{R}^n\). Zbl 0927.52007Alesker, S.; Dar, S.; Milman, V. 14 1999 The covering numbers and “low \(M^*\)-estimate” for quasi-convex bodies. Zbl 0948.52005Litvak, A. E.; Milman, V. D.; Pajor, A. 9 1999 An “isomorphic” version of Dvoretzky’s theorem. II. Zbl 0942.46012Milman, Vitali; Schechtman, Gideon 7 1999 Asymptotic versions of operators and operator ideals. Zbl 0932.47051Milman, Vitali; Wagner, Roy 1 1999 Entropy methods in asymptotic convex geometry. Zbl 0964.52006Milman, Vitali; Pajor, Alain 1 1999 Averages of norms and quasi-norms. Zbl 0920.46006Litvak, A. E.; Milman, V. D.; Schechtman, G. 33 1998 Mean width and diameter of proportional sections of a symmetric convex body. Zbl 0896.52007Giannopoulos, A. A.; Milman, V. D. 12 1998 Randomness and pattern in convex geometric analysis. Zbl 0911.52003Milman, Vitali 3 1998 Surprising geometric phenomena in high-dimensional convexity theory. Zbl 0938.52006Milman, V. 2 1998 Global versus local asymptotic theories of finite-dimensional normed spaces. Zbl 0911.52002Milman, V. D.; Schechtman, G. 121 1997 On the diameter of proportional sections of a symmetric convex body. Zbl 0877.52009Giannopoulos, A. A.; Milman, V. D. 11 1997 How small can the intersection of a few rotations of a symmetric convex body be? Zbl 0889.52003Giannopoulos, Apostolos A.; Milman, Vitali D. 5 1997 Averages of norms and behavior of families of projective caps on the sphere. Zbl 0891.52002Litvak, A. E.; Milman, V. D.; Schechtman, G. 1 1997 Asymptotic infinite-dimensional theory of Banach spaces. Zbl 0872.46013Maurey, B.; Milman, V. D.; Tomczak-Jaegermann, N. 36 1995 An “isomorphic” version of Dvoretzky’s theorem. Zbl 0836.46007Milman, Vitali D.; Schechtman, Gideon 7 1995 Isomorphic Euclidean regularization of quasi-norms in \(\mathbb{R}^ n\). Zbl 0853.52001Milman, Vitali 2 1995 The local theory of normed spaces and its applications to convexity. Zbl 0791.52003Lindenstrauss, J.; Milman, V. D. 26 1993 ...and 74 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,779 Authors 64 Milman, Vitali D. 35 Naor, Assaf 35 Tomczak-Jaegermann, Nicole 31 Artstein-Avidan, Shiri 31 Paouris, Grigoris 27 Klartag, Bo’az 27 Mendelson, Shahar 23 Pajor, Alain 22 Giannopoulos, Apostolos A. 21 Werner, Elisabeth M. 20 Alonso-Gutiérrez, David 20 Bainov, Drumi Dimitrov 20 Bobkov, Sergey Germanovich 20 Bourgain, Jean 20 Litvak, Aleksandr Evgen’evich 19 Milman, Emanuel 19 Prochno, Joscha 18 Alon, Noga 17 Fradelizi, Matthieu 17 Guédon, Olivier 17 König, Hermann 17 Schechtman, Gideon 17 Szarek, Stanislaw Jerzy 15 Rotem, Liran 15 Vershynin, Roman 15 Zvavitch, Artem 14 Meyer, Mathieu 14 Schlumprecht, Thomas 13 Henk, Martin 13 Temlyakov, Vladimir Nikolaevich 12 Huang, Qingzhong 12 Koldobsky, Alexander L. 12 Li, Aijun 12 Mendel, Manor 11 Brazitikos, Silouanos 11 Pestov, Vladimir G. 11 Rudelson, Mark 11 Schütt, Carsten 11 Xiong, Ge 10 Barthe, Franck 10 Böröczky, Karoly jun. 10 Funano, Kei 10 Johnson, William Buhmann 10 Motakis, Pavlos 10 Odell, Edward 10 Slomka, Boaz A. 10 Thäle, Christoph 10 Valettas, Petros 10 Ye, Deping 9 Argyros, Spiros A. 9 Bastero, Jesús 9 Leng, Gangsong 9 Merino, Bernardo González 9 Pivovarov, Peter 9 Tikhomirov, Konstantin E. 9 Villa, Rafael 8 Aubrun, Guillaume 8 Colesanti, Andrea 8 Mohar, Bojan 8 Naszódi, Márton 8 Pisier, Gilles 8 Tsolomitis, Antonis 8 Zhang, Gaoyong 7 Astashkin, Sergeĭ Vladimir 7 Ball, Keith Martin 7 Bollobás, Béla 7 Carl, Bernd 7 Gordon, Yehoram 7 He, Binwu 7 Hinrichs, Aicke 7 Jiménez, Carlos Hugo 7 Ledoux, Michel 7 Lee, James R. 7 Li, Hanfeng 7 Lopez-Abad, Jordi 7 Matoušek, Jiří 7 Schmuckenschläger, Michael 7 Schneider, Friedrich Martin 6 Adamczak, Radosław 6 Castillo, Jesús M. F. 6 Chasapis, Giorgos 6 Dilworth, Stephen J. 6 Ferenczi, Valentin 6 Friedland, Omer 6 Gluskin, Efim D. 6 Huang, Han 6 Jeribi, Aref 6 Kabluchko, Zakhar A. 6 Kerr, David 6 Kolesnikov, Alexander V. 6 Kushpel, Alexander K. 6 Liu, Shiping 6 Lubotzky, Alexander 6 Ludwig, Monika 6 Lutwak, Erwin 6 Ma, Tongyi 6 Madiman, Mokshay M. 6 Mbombo, Brice R. 6 Mussnig, Fabian 6 Ouahab, Abdelghani ...and 1,679 more Authors all top 5 Cited in 355 Serials 127 Israel Journal of Mathematics 112 Journal of Functional Analysis 89 Advances in Mathematics 69 Journal of Mathematical Analysis and Applications 69 Proceedings of the American Mathematical Society 39 Transactions of the American Mathematical Society 39 Discrete & Computational Geometry 28 The Annals of Probability 28 Geometric and Functional Analysis. 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Series B 4 Journal of Convex Analysis 4 Electronic Journal of Probability 4 Mathematical Inequalities & Applications 4 Journal of Topology and Analysis ...and 255 more Serials all top 5 Cited in 55 Fields 601 Convex and discrete geometry (52-XX) 554 Functional analysis (46-XX) 339 Probability theory and stochastic processes (60-XX) 285 Combinatorics (05-XX) 150 Operator theory (47-XX) 113 Differential geometry (53-XX) 112 Real functions (26-XX) 99 Computer science (68-XX) 93 Ordinary differential equations (34-XX) 65 Information and communication theory, circuits (94-XX) 63 Linear and multilinear algebra; matrix theory (15-XX) 60 Measure and integration (28-XX) 55 Partial differential equations (35-XX) 51 Calculus of variations and optimal control; optimization (49-XX) 49 Approximations and expansions (41-XX) 48 Harmonic analysis on Euclidean spaces (42-XX) 47 Dynamical systems and ergodic theory (37-XX) 47 General topology (54-XX) 45 Quantum theory (81-XX) 43 Geometry (51-XX) 43 Operations research, mathematical programming (90-XX) 41 Numerical analysis (65-XX) 39 Abstract harmonic analysis (43-XX) 39 Statistics (62-XX) 37 Global analysis, analysis on manifolds (58-XX) 35 Number theory (11-XX) 35 Topological groups, Lie groups (22-XX) 33 Group theory and generalizations (20-XX) 30 Difference and functional equations (39-XX) 26 Statistical mechanics, structure of matter (82-XX) 24 Mathematical logic and foundations (03-XX) 19 Functions of a complex variable (30-XX) 19 Manifolds and cell complexes (57-XX) 17 Several complex variables and analytic spaces (32-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Order, lattices, ordered algebraic structures (06-XX) 14 Algebraic geometry (14-XX) 14 Algebraic topology (55-XX) 14 Systems theory; control (93-XX) 13 Biology and other natural sciences (92-XX) 10 General and overarching topics; collections (00-XX) 10 Integral transforms, operational calculus (44-XX) 7 History and biography (01-XX) 5 Integral equations (45-XX) 3 Field theory and polynomials (12-XX) 3 Potential theory (31-XX) 3 Special functions (33-XX) 3 Mechanics of particles and systems (70-XX) 3 Mechanics of deformable solids (74-XX) 2 Nonassociative rings and algebras (17-XX) 2 Sequences, series, summability (40-XX) 1 Commutative algebra (13-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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