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Milman, Vitali D.

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Author ID: milman.vitali-d Recent zbMATH articles by "Milman, Vitali D."
Published as: Milman, V. D.; Milman, Vitali; Mil’man, V. D.; Milman, Vitali D.; Milman, V.; Mil’man, Vitali D.
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Documents Indexed: 231 Publications since 1960, including 24 Books
all top 5

Co-Authors

54 single-authored
26 Artstein-Avidan, Shiri
20 König, Hermann
18 Bourgain, Jean
13 Lindenstrauss, Joram
13 Tomczak-Jaegermann, Nicole
11 Giannopoulos, Apostolos A.
11 Schechtman, Gideon
10 Pajor, Alain
9 Alon, Noga M.
9 Litvak, Aleksandr Evgen’evich
9 Rotem, Liran
8 Klartag, Bo’az
7 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.
3 Figiel, Tadeusz
3 Friedland, Omer
3 Gluskin, Efim D.
3 Myshkis, Anatoliĭ Dmitrievich
3 Pisier, Gilles
3 Segal, Alexander
3 Wolfson, Haim J.
2 Amir, Dan
2 Ball, Keith Martin
2 Kononenko, A. I.
2 Schneider, Rolf G.
2 Sharir, Micha
2 Tsolomitis, Antonis
2 Wagner, Roy
1 Aron, Richard M.
1 Ben-Efraim, Limor
1 Benyamini, Yoav
1 Curbera, Guillermo P.
1 Davis, William Jay
1 Deza, Michel Marie
1 Dineen, Seán
1 Eidelman, Yuli
1 Eliashberg, Yakov Matveevich
1 Enflo, Per H.
1 Galil, Zvi
1 Ghoussoub, Nassif A.
1 Johnson, William Buhmann
1 Lev, A. Ju.
1 Lindenstrauss, Ayelet
1 Lindenstrauss, Elon
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 Schoen, Richard Melvin
1 Slomka, Boaz A.
1 Sodin, Mikhail
1 Sodin, Sasha
1 Szankowski, Andrzej
1 Tkachenko, Vadim Aleksandrovich
1 Tumarkin, Yu. B.
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 St. Petersburg Mathematical Journal
2 Acta Mathematica
2 Geometriae Dedicata
2 Inventiones Mathematicae
2 Sibirskiĭ Matematicheskiĭ Zhurnal
2 Geometric and Functional Analysis. GAFA
2 Notices of the American Mathematical Society
2 Annals of Mathematics. Second Series
2 Advances in Geometry
2 Journal of Mathematical Physics, Analysis, Geometry
2 Mathematical Sciences Research Institute Publications
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 Mathematical Surveys and Monographs
1 Proceedings of the Steklov Institute of Mathematics
1 Translations. Series 2. American Mathematical Society
1 Operator Theory: Advances and Applications

Publications by Year

Citations contained in zbMATH Open

166 Publications have been cited 2,559 times in 1,604 Documents Cited by Year
Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds. Zbl 0606.46013
Milman, Vitali D.; Schechtman, Gideon
245
1986
\(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators. Zbl 0549.05051
Alon, N.; Milman, V. D.
219
1985
The dimension of almost spherical sections of convex bodies. Zbl 0375.52002
Figiel, T.; Lindenstrauss, J.; Milman, V. D.
139
1977
A topological application of the isoperimetric inequality. Zbl 0522.53039
Gromov, Mikhael; Milman, V. D.
128
1983
Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed \(n\)-dimensional space. Zbl 0679.46012
Milman, V. D.; Pajor, A.
127
1989
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\). Zbl 0617.52006
Bourgain, J.; Milman, V. D.
124
1987
Global versus local asymptotic theories of finite-dimensional normed spaces. Zbl 0911.52002
Milman, V. D.; Schechtman, G.
102
1997
On the stability of motion in the presence of impulses. Zbl 1358.34022
Mil’man, V. D.; Myškis, A. D.
79
1960
Asymptotic geometric analysis. I. Zbl 1337.52001
Artstein-Avidan, Shiri; Giannopoulos, Apostolos; Milman, Vitali D.
74
2015
The Santaló point of a function, and a functional form of the Santaló inequality. Zbl 1121.52021
Artstein-Avidan, S.; Klartag, B.; Milman, V.
58
2004
Approximation of zonoids by zonotopes. Zbl 0682.46008
Bourgain, J.; Lindenstrauss, J.; Milman, V.
53
1989
Geometry of log-concave functions and measures. Zbl 1099.28002
Klartag, B.; Milman, V. D.
49
2005
Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces. Zbl 0623.46007
Gromov, M.; Milman, V. D.
42
1987
Extremal problems and isotropic positions of convex bodies. Zbl 0964.52004
Giannopoulos, A. A.; Milman, V. D.
41
2000
Entropy and asymptotic geometry of non-symmetric convex bodies. Zbl 0974.52004
Milman, V. D.; Pajor, A.
36
2000
The concept of duality in convex analysis, and the characterization of the Legendre transform. Zbl 1173.26008
Artstein-Avidan, Shiri; Milman, Vitali
33
2009
Averages of norms and quasi-norms. Zbl 0920.46006
Litvak, A. E.; Milman, V. D.; Schechtman, G.
32
1998
On type of metric spaces. Zbl 0617.46024
Bourgain, J.; Milman, V.; Wolfson, H.
32
1986
Asymptotic infinite-dimensional theory of Banach spaces. Zbl 0872.46013
Maurey, B.; Milman, V. D.; Tomczak-Jaegermann, N.
29
1995
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 0604.52003
Milman, Vitali D.
29
1986
Euclidean structure in finite dimensional normed spaces. Zbl 1009.46004
Giannopoulos, Apostolos A.; Milman, Vitali D.
28
2001
The local theory of normed spaces and its applications to convexity. Zbl 0791.52003
Lindenstrauss, J.; Milman, V. D.
23
1993
Geometric theory of Banach spaces. Part I: The theory of basis and minimal systems. Zbl 0221.46015
Mil’man, V. D.
21
1970
Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space. Zbl 0581.46014
Milman, V. D.
21
1985
Unconditional and symmetric sets in \(n\)-dimensional normed spaces. Zbl 0445.46011
Amir, D.; Milman, V. D.
20
1980
Coordinate density of sets of vectors. Zbl 0401.05015
Karpovsky, M. G.; Milman, V. D.
20
1978
Better expanders and superconcentrators. Zbl 0641.68102
Alon, N.; Galil, Z.; Milman, V. D.
20
1987
The concept of duality for measure projections of convex bodies. Zbl 1145.26003
Artstein-Avidan, Shiri; Milman, Vitali
20
2008
Some properties of strictly singular operators. Zbl 0179.17801
Mil’man, V. D.
20
1969
Banach spaces with a weak cotype 2 property. Zbl 0611.46022
Milman, Vitali D.; Pisier, Gilles
18
1986
Duality of metric entropy. Zbl 1072.52001
Artstein, S.; Milman, V.; Szarek, S. J.
17
2004
Concentration property on probability spaces. Zbl 1068.28002
Giannopoulos, A. A.; Milman, V. D.
16
2000
Symmetrization and isotropic constants of convex bodies. Zbl 1070.52002
Bourgain, J.; Klartag, B.; Milman, V.
16
2004
Minkowski sums and symmetrizations. Zbl 0645.52001
Bourgain, J.; Lindenstrauss, J.; Milman, V. D.
16
1988
Asymptotic \(\ell_ p\) spaces and bounded distortions. Zbl 0822.46007
Milman, Vitali D.; Tomczak-Jaegermann, Nicole
15
1993
Asymptotic formulas for the diameter of sections of symmetric convex bodies. Zbl 1088.46006
Giannopoulos, Apostolos; Milman, Vitali D.; Tsolomitis, Antonis
15
2005
Hidden structures in the class of convex functions and a new duality transform. Zbl 1221.26018
Artstein-Avidan, Shiri; Milman, Vitali
14
2011
Functional analysis. An introduction. Zbl 1077.46001
Eidelman, Yuli; Milman, Vitali; Tsolomitis, Antonis
14
2004
Mixed integrals and related inequalities. Zbl 1267.26021
Milman, Vitali; Rotem, Liran
13
2013
Embedding of \(\ell^ k_{\infty}\) in finite dimensional Banach spaces. Zbl 0546.46015
Alon, N.; Milman, V. D.
13
1983
On Hilbertian subsets of finite metric spaces. Zbl 0634.46008
Bourgain, J.; Figiel, T.; Milman, V.
12
1986
Gaussian processes and mixed volumes. Zbl 0636.60036
Milman, V. D.; Pisier, G.
12
1987
A characterization of the concept of duality. Zbl 1140.52300
Artstein-Avidan, Shiri; Milman, Vitali
12
2008
Convex bodies with minimal mean width. Zbl 0978.52001
Giannopoulos, A. A.; Milman, V. D.; Rudelson, M.
11
2000
Mean width and diameter of proportional sections of a symmetric convex body. Zbl 0896.52007
Giannopoulos, A. A.; Milman, V. D.
11
1998
The M-ellipsoid, symplectic capacities and volume. Zbl 1138.53060
Artstein-Avidan, Shiri; Milman, Vitali; Ostrover, Yaron
11
2008
A remarkable measure preserving diffeomorphism between two convex bodies in \(\mathbb{R}^n\). Zbl 0927.52007
Alesker, S.; Dar, S.; Milman, V.
10
1999
Geometrization of probability. Zbl 1154.60022
Milman, Vitali D.
10
2008
The chain rule as a functional equation. Zbl 1203.39014
Artstein-Avidan, Shiri; König, Hermann; Milman, Vitali
9
2010
Characterizing the derivative and the entropy function by the Leibniz rule. Zbl 1231.39011
König, Hermann; Milman, Vitali
9
2011
On the diameter of proportional sections of a symmetric convex body. Zbl 0877.52009
Giannopoulos, A. A.; Milman, V. D.
9
1997
The covering numbers and “low \(M^*\)-estimate” for quasi-convex bodies. Zbl 0948.52005
Litvak, A. E.; Milman, V. D.; Pajor, A.
9
1999
Regularization of star bodies by random hyperplane cut off. Zbl 1076.46008
Milman, V. D.; Pajor, A.
9
2003
Some applications of duality relations. Zbl 0818.46016
Milman, V.
9
1991
Geometric theory of Banach spaces. II: Geometry of the unit sphere. Zbl 0238.46012
Mil’man, V. D.
9
1972
Sections euclidiennes et volume des corps symétriques convexes dans \(R^ n\). (Euclidean sections and volume of symmetric convex bodies in \(R^ n.)\). Zbl 0576.52002
Bourgain, Jean; Milman, Vitali D.
9
1985
A characterization of the support map. Zbl 1192.52004
Artstein-Avidan, S.; Milman, V.
8
2010
Brunn theorem and a concentration of volume phenomena for symmetric convex bodies. Zbl 0953.52500
Gromov, M.; Milman, V. D.
8
1984
Geometric probability and random cotype 2. Zbl 1087.46006
Gluskin, E.; Milman, V.
8
2004
Estimates related to Steiner symmetrizations. Zbl 0673.52001
Bourgain, J.; Lindenstrauss, J.; Milman, V.
8
1989
Rapid Steiner symmetrization of most of a convex body and the slicing problem. Zbl 1084.52003
Klartag, B.; Milman, V.
8
2005
The heritage of P. Lévy in geometrical functional analysis. Zbl 0681.46021
Milman, V. D.
8
1988
A characterization of product preserving maps with applications to a characterization of the Fourier transform. Zbl 1272.42004
Alesker, S.; Artstein-Avidan, S.; Faifman, D.; Milman, V.
8
2010
An “isomorphic” version of Dvoretzky’s theorem. Zbl 0836.46007
Milman, Vitali D.; Schechtman, Gideon
7
1995
Topics in asymptotic geometric analysis. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.46010
Milman, V.
7
2000
An “isomorphic” version of Dvoretzky’s theorem. II. Zbl 0942.46012
Milman, Vitali; Schechtman, Gideon
7
1999
On a geometric inequality. Zbl 0653.46015
Bourgain, J.; Meyer, M.; Milman, V.; Pajor, A.
7
1988
Geometric applications of Chernoff-type estimates and a zigzag approximation for balls. Zbl 1119.46012
Artstein-Avidan, S.; Friedland, O.; Milman, V.
7
2006
Infinite-dimensional geometry of the unit sphere in Banach space. Zbl 0175.13201
Mil’man, V. D.
7
1967
Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality. Zbl 0588.46013
Milman, V. D.
7
1985
Isomorphic Steiner symmetrization. Zbl 1034.52008
Klartag, B.; Milman, V. D.
6
2003
A new proof of the Maurey-Pisier theorem. Zbl 0418.46010
Milman, V. D.; Sharir, M.
6
1979
Polynomial bounds for large Bernoulli sections of \(\ell_1^N\). Zbl 1160.60004
Artstein-Avidan, Shiri; Friedland, Omer; Milman, Vitali; Sodin, Sasha
6
2006
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 1381.52006
Milman, Vitali; Rotem, Liran
6
2017
Minkowski spaces with extremal distance from the Euclidean space. Zbl 0374.46013
Milman, V. D.; Wolfson, H.
6
1978
The geometry of nested families with empty intersection. Structure of the unit sphere of a nonreflexive space. Zbl 0196.13501
Mil’man, D. P.; Mil’man, V. D.
6
1969
Dichotomie du cotype pour les espaces invariants. (Dichotomy of cotype for invariant spaces). Zbl 0584.43005
Bourgain, Jean; Milman, Vitali
6
1985
Dvoretzky’s theorem – thirty years later. Zbl 0787.46016
Milman, V.
5
1992
How small can the intersection of a few rotations of a symmetric convex body be? Zbl 0889.52003
Giannopoulos, Apostolos A.; Milman, Vitali D.
5
1997
The distance between certain \(n\)-dimensional Banach spaces. Zbl 0475.46010
Davis, W. J.; Milman, V. D.; Tomczak-Jaegermann, Nicole
5
1981
Shrinking minimal systems and complementation of \(\ell^n_p\)-spaces in reflexive Banach spaces. Zbl 0418.46009
Milman, V. D.; Sharir, M.
5
1979
On convexified packing and entropy duality. Zbl 1062.52023
Artstein, S.; Milman, V.; Szarek, S.; Tomczak-Jaegermann, N.
5
2004
Asymptotic convex geometry – short overview. Zbl 1068.52011
Giannopoulos, A. A.; Milman, V. D.
5
2004
A quantitative finite-dimensional Krivine theorem. Zbl 0612.46021
Amir, D.; Milman, V. D.
5
1985
Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. Zbl 1111.52009
Artstein-Avidan, S.; Milman, V. D.
5
2006
A note on a low \(M^*\)-estimate. Zbl 0760.46009
Milman, V.
5
1991
Random shocks in linear dynamical systems. Zbl 0133.10403
Mil’man, V. D.; Myshkis, A. D.
5
1963
Die geometrische Theorie der Banachräume. II: Die Geometrie der Einheitssphäre. (Geometric theory of Banach spaces. II: Geometry of the unit sphere). Zbl 0229.46017
Mil’man, V. D.
5
1971
Asymptotic properties of functions of several variables defined on homogeneous spaces. Zbl 0236.26009
Mil’man, V. D.
5
1971
New proof of the theorem of A. Dvoretzky on intersections of convex bodies. Zbl 0239.46018
Mil’man, V. D.
5
1972
Geometrical inequalities and mixed volumes in the local theory of Banach spaces. Zbl 0582.46015
Milman, V. D.
5
1985
The dimension of almost spherical sections of convex bodies. Zbl 0329.52003
Figiel, T.; Lindenstrauss, J.; Milman, V. D.
4
1976
A characterization of the Fourier transform and related topics. Zbl 1184.42009
Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali
4
2009
A characterization of duality through section/projection correspondence in the finite dimensional setting. Zbl 1258.52002
Milman, Vitali D.; Segal, Alexander; Slomka, Boaz A.
4
2011
A geometric lemma and duality of entropy numbers. Zbl 0987.46017
Milman, V. D.; Szarek, S. J.
4
2000
Note on the geometric-arithmetic mean inequality. Zbl 1035.26020
Gluskin, E.; Milman, V.
4
2003
Isomorphic symmetrization and geometric inequalities. Zbl 0652.52008
Milman, V. D.
4
1988
Geometric applications of Chernoff-type estimates. Zbl 1146.46004
Artstein-Avidan, S.; Friedland, O.; Milman, V.
4
2007
An operator equation generalizing the Leibniz rule for the second derivative. Zbl 1262.39031
König, Hermann; Milman, Vitali
4
2012
Rigidity and stability of the Leibniz and the chain rule. Zbl 1301.39016
König, Hermann; Milman, Vitali
4
2013
Weighted geometric means of convex bodies. Zbl 1430.52003
Milman, Vitali; Rotem, Liran
2
2019
Tribute to Joe Diestel (1943–2017). Zbl 1398.01023
Aron, Richard; Dineen, Seán; Milman, Vitali; Enflo, Per; Curbera, Guillermo P.
1
2018
“Irrational” constructions in convex geometry. Zbl 1394.52004
Milman, V.; Rotem, L.
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 1381.52006
Milman, Vitali; Rotem, Liran
6
2017
Powers and logarithms of convex bodies. (Puissances et logarithmes de corps convexes.) Zbl 1380.52008
Milman, Vitali; Rotem, Liran
3
2017
A characterization of the mixed discriminant. Zbl 1341.15004
Florentin, D.; Milman, V. D.; Schneider, R.
2
2016
Asymptotic geometric analysis. I. Zbl 1337.52001
Artstein-Avidan, Shiri; Giannopoulos, Apostolos; Milman, Vitali D.
74
2015
Characterizing addition of convex sets by polynomiality of volume and by the homothety operation. Zbl 1316.52004
Milman, Vitali; Rotem, Liran
4
2015
Submultiplicative functions and operator inequalities. Zbl 1317.39034
König, Hermann; Milman, Vitali
2
2014
On the oscillation rigidity of a Lipschitz function on a high-dimensional flat torus. Zbl 1323.46010
Faifman, Dmitry; Klartag, Bo’az; Milman, Vitali
1
2014
The derivation equation for \(C^k\)-functions: stability and localization. Zbl 1308.39019
König, Hermann; Milman, Vitali
1
2014
Mixed integrals and related inequalities. Zbl 1267.26021
Milman, Vitali; Rotem, Liran
13
2013
Rigidity and stability of the Leibniz and the chain rule. Zbl 1301.39016
König, Hermann; Milman, Vitali
4
2013
\(\alpha\)-concave functions and a functional extension of mixed volumes. Zbl 1277.52011
Milman, Vitali; Rotem, Liran
3
2013
Operator functional equations in analysis. Zbl 1266.39024
König, Hermann; Milman, Vitali
2
2013
Stability results for some classical convexity operations. Zbl 1268.52007
Artstein-Avidan, Shiri; Milman, Vitali
1
2013
An operator equation characterizing the Laplacian. Zbl 1273.47035
König, H.; Milman, V.
1
2013
An operator equation generalizing the Leibniz rule for the second derivative. Zbl 1262.39031
König, Hermann; Milman, Vitali
4
2012
On multiplicative maps of continuous and smooth functions. Zbl 1267.39016
Artstein-Avidan, Shiri; Faifman, Dmitry; Milman, Vitali
3
2012
Order isomorphisms on convex functions in windows. Zbl 1266.26021
Artstein-Avidan, Shiri; Florentin, Dan; Milman, Vitali
3
2012
Hidden structures in the class of convex functions and a new duality transform. Zbl 1221.26018
Artstein-Avidan, Shiri; Milman, Vitali
14
2011
Characterizing the derivative and the entropy function by the Leibniz rule. Zbl 1231.39011
König, Hermann; Milman, Vitali
9
2011
A characterization of duality through section/projection correspondence in the finite dimensional setting. Zbl 1258.52002
Milman, Vitali D.; Segal, Alexander; Slomka, Boaz A.
4
2011
Characterizing the mixed volume. Zbl 1242.52011
Milman, Vitali D.; Schneider, Rolf
3
2011
Order isomorphisms in windows. Zbl 1225.26023
Artstein-Avidan, Shiri; Florentin, Dan; Milman, Vitali
2
2011
A functional equation characterizing the second derivative. Zbl 1226.39009
König, Hermann; Milman, Vitali
1
2011
The chain rule as a functional equation. Zbl 1203.39014
Artstein-Avidan, Shiri; König, Hermann; Milman, Vitali
9
2010
A characterization of the support map. Zbl 1192.52004
Artstein-Avidan, S.; Milman, V.
8
2010
A characterization of product preserving maps with applications to a characterization of the Fourier transform. Zbl 1272.42004
Alesker, S.; Artstein-Avidan, S.; Faifman, D.; Milman, V.
8
2010
Essentially-Euclidean convex bodies. Zbl 1200.46019
Litvak, 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
Alon, Noga; Bourgain, Jean; Connes, Alain; Gromov, Mikhael; Milman, Vitali D.
1
2010
The concept of duality in convex analysis, and the characterization of the Legendre transform. Zbl 1173.26008
Artstein-Avidan, Shiri; Milman, Vitali
33
2009
A characterization of the Fourier transform and related topics. Zbl 1184.42009
Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali
4
2009
The concept of duality for measure projections of convex bodies. Zbl 1145.26003
Artstein-Avidan, Shiri; Milman, Vitali
20
2008
A characterization of the concept of duality. Zbl 1140.52300
Artstein-Avidan, Shiri; Milman, Vitali
12
2008
The M-ellipsoid, symplectic capacities and volume. Zbl 1138.53060
Artstein-Avidan, Shiri; Milman, Vitali; Ostrover, Yaron
11
2008
Geometrization of probability. Zbl 1154.60022
Milman, Vitali D.
10
2008
A characterization of the Fourier transform and related topics. Zbl 1283.42008
Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali
3
2008
Using Rademacher permutations to reduce randomness. Zbl 1131.60004
Artstein-Avidan, S.; Milman, V. D.
1
2008
Geometric applications of Chernoff-type estimates. Zbl 1146.46004
Artstein-Avidan, S.; Friedland, O.; Milman, V.
4
2007
On the Euclidean metric entropy of convex bodies. Zbl 1132.52006
Litvak, 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 1119.46012
Artstein-Avidan, S.; Friedland, O.; Milman, V.
7
2006
Polynomial bounds for large Bernoulli sections of \(\ell_1^N\). Zbl 1160.60004
Artstein-Avidan, Shiri; Friedland, Omer; Milman, Vitali; Sodin, Sasha
6
2006
Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. Zbl 1111.52009
Artstein-Avidan, S.; Milman, V. D.
5
2006
Entropy extension. Zbl 1118.52014
Litvak, A. E.; Milman, V. D.; Pajor, A.; Tomczak-Jaegermann, N.
1
2006
Geometry of log-concave functions and measures. Zbl 1099.28002
Klartag, B.; Milman, V. D.
49
2005
Asymptotic formulas for the diameter of sections of symmetric convex bodies. Zbl 1088.46006
Giannopoulos, Apostolos; Milman, Vitali D.; Tsolomitis, Antonis
15
2005
Rapid Steiner symmetrization of most of a convex body and the slicing problem. Zbl 1084.52003
Klartag, B.; Milman, V.
8
2005
The Santaló point of a function, and a functional form of the Santaló inequality. Zbl 1121.52021
Artstein-Avidan, S.; Klartag, B.; Milman, V.
58
2004
Duality of metric entropy. Zbl 1072.52001
Artstein, S.; Milman, V.; Szarek, S. J.
17
2004
Symmetrization and isotropic constants of convex bodies. Zbl 1070.52002
Bourgain, J.; Klartag, B.; Milman, V.
16
2004
Functional analysis. An introduction. Zbl 1077.46001
Eidelman, Yuli; Milman, Vitali; Tsolomitis, Antonis
14
2004
Geometric probability and random cotype 2. Zbl 1087.46006
Gluskin, E.; Milman, V.
8
2004
On convexified packing and entropy duality. Zbl 1062.52023
Artstein, S.; Milman, V.; Szarek, S.; Tomczak-Jaegermann, N.
5
2004
Asymptotic convex geometry – short overview. Zbl 1068.52011
Giannopoulos, A. A.; Milman, V. D.
5
2004
Isomorphic random subspaces and quotients of convex and quasi-convex bodies. Zbl 1071.52007
Litvak, A. E.; Milman, V. D.; Tomczak-Jaegermann, N.
1
2004
Essential uniqueness of an M-ellipsoid of a given convex body. Zbl 1067.52005
Milman, V. D.; Pajor, A.
1
2004
Regularization of star bodies by random hyperplane cut off. Zbl 1076.46008
Milman, V. D.; Pajor, A.
9
2003
Isomorphic Steiner symmetrization. Zbl 1034.52008
Klartag, B.; Milman, V. D.
6
2003
Note on the geometric-arithmetic mean inequality. Zbl 1035.26020
Gluskin, E.; Milman, V.
4
2003
A reduction of the slicing problem to finite volume ratio bodies. Zbl 1036.52005
Bourgain, Jean; Klartag, Bo’az; Milman, Vitali
3
2003
Some remarks on a lemma of Ran Raz. Zbl 1070.46009
Milman, Vitali; Wagner, Roy
2
2003
Duality of metric entropy in Euclidean space. Zbl 1042.52002
Artstein, Shiri; Milman, Vitali D.; Szarek, Stanislaw J.
2
2003
More on the duality conjecture for entropy numbers. Zbl 1042.52001
Artstein, 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
Milman, V. D.; Schechtman, G.
1
2003
Randomizing properties of convex high-dimensional bodies and some geometric inequalities. Zbl 1019.46009
Gluskin, Efim; Milman, Vitali
2
2002
Euclidean structure in finite dimensional normed spaces. Zbl 1009.46004
Giannopoulos, Apostolos A.; Milman, Vitali D.
28
2001
A geometric approach to duality of metric entropy. Zbl 0983.46013
Milman, Vitali D.; Szarek, Stanislaw J.
1
2001
Extremal problems and isotropic positions of convex bodies. Zbl 0964.52004
Giannopoulos, A. A.; Milman, V. D.
41
2000
Entropy and asymptotic geometry of non-symmetric convex bodies. Zbl 0974.52004
Milman, V. D.; Pajor, A.
36
2000
Concentration property on probability spaces. Zbl 1068.28002
Giannopoulos, A. A.; Milman, V. D.
16
2000
Convex bodies with minimal mean width. Zbl 0978.52001
Giannopoulos, A. A.; Milman, V. D.; Rudelson, M.
11
2000
Topics in asymptotic geometric analysis. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.46010
Milman, V.
7
2000
A geometric lemma and duality of entropy numbers. Zbl 0987.46017
Milman, V. D.; Szarek, S. J.
4
2000
Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 1996–2000. Zbl 0949.00025
Milman, V. D.; Schechtman, G.
1
2000
Stabilized asymptotic structures and envelopes in Banach spaces. Zbl 0987.46025
Milman, V. D.; Tomczak-Jaegermann, N.
1
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
Alon, N.; Bourgain, Jean; Connes, A.; Gromov, M.; Milman, V.
1
2000
A remarkable measure preserving diffeomorphism between two convex bodies in \(\mathbb{R}^n\). Zbl 0927.52007
Alesker, S.; Dar, S.; Milman, V.
10
1999
The covering numbers and “low \(M^*\)-estimate” for quasi-convex bodies. Zbl 0948.52005
Litvak, A. E.; Milman, V. D.; Pajor, A.
9
1999
An “isomorphic” version of Dvoretzky’s theorem. II. Zbl 0942.46012
Milman, Vitali; Schechtman, Gideon
7
1999
Entropy methods in asymptotic convex geometry. Zbl 0964.52006
Milman, Vitali; Pajor, Alain
1
1999
Asymptotic versions of operators and operator ideals. Zbl 0932.47051
Milman, Vitali; Wagner, Roy
1
1999
Averages of norms and quasi-norms. Zbl 0920.46006
Litvak, A. E.; Milman, V. D.; Schechtman, G.
32
1998
Mean width and diameter of proportional sections of a symmetric convex body. Zbl 0896.52007
Giannopoulos, A. A.; Milman, V. D.
11
1998
Randomness and pattern in convex geometric analysis. Zbl 0911.52003
Milman, Vitali
3
1998
Surprising geometric phenomena in high-dimensional convexity theory. Zbl 0938.52006
Milman, V.
2
1998
Global versus local asymptotic theories of finite-dimensional normed spaces. Zbl 0911.52002
Milman, V. D.; Schechtman, G.
102
1997
On the diameter of proportional sections of a symmetric convex body. Zbl 0877.52009
Giannopoulos, A. A.; Milman, V. D.
9
1997
How small can the intersection of a few rotations of a symmetric convex body be? Zbl 0889.52003
Giannopoulos, Apostolos A.; Milman, Vitali D.
5
1997
Averages of norms and behavior of families of projective caps on the sphere. Zbl 0891.52002
Litvak, A. E.; Milman, V. D.; Schechtman, G.
1
1997
Asymptotic infinite-dimensional theory of Banach spaces. Zbl 0872.46013
Maurey, B.; Milman, V. D.; Tomczak-Jaegermann, N.
29
1995
An “isomorphic” version of Dvoretzky’s theorem. Zbl 0836.46007
Milman, Vitali D.; Schechtman, Gideon
7
1995
Isomorphic Euclidean regularization of quasi-norms in \(\mathbb{R}^ n\). Zbl 0853.52001
Milman, Vitali
2
1995
The local theory of normed spaces and its applications to convexity. Zbl 0791.52003
Lindenstrauss, J.; Milman, V. D.
23
1993
Asymptotic \(\ell_ p\) spaces and bounded distortions. Zbl 0822.46007
Milman, Vitali D.; Tomczak-Jaegermann, Nicole
15
1993
Dvoretzky’s theorem – thirty years later. Zbl 0787.46016
Milman, V.
5
1992
Some applications of duality relations. Zbl 0818.46016
Milman, V.
9
1991
A note on a low \(M^*\)-estimate. Zbl 0760.46009
Milman, V.
5
1991
Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 1989-90. Zbl 0755.00015
Lindenstrauss, Joram; Milman, Vitali D.
1
1991
Spectrum of a position of a convex body and linear duality relations. Zbl 0705.46005
Milman, V.
2
1990
...and 66 more Documents
all top 5

Cited by 1,503 Authors

62 Milman, Vitali D.
35 Tomczak-Jaegermann, Nicole
33 Naor, Assaf
28 Paouris, Grigoris
27 Artstein-Avidan, Shiri
25 Klartag, Bo’az
25 Mendelson, Shahar
23 Pajor, Alain
21 Giannopoulos, Apostolos A.
20 Bobkov, Sergey Germanovich
20 Bourgain, Jean
20 Litvak, Aleksandr Evgen’evich
19 Bainov, Drumi Dimitrov
18 Alonso-Gutiérrez, David
18 Werner, Elisabeth M.
17 Alon, Noga M.
17 König, Hermann
17 Schechtman, Gideon
16 Guédon, Olivier
16 Milman, Emanuel
16 Szarek, Stanislaw Jerzy
15 Fradelizi, Matthieu
15 Prochno, Joscha
15 Vershynin, Roman
13 Meyer, Mathieu
13 Zvavitch, Artem
12 Henk, Martin
12 Mendel, Manor
12 Rotem, Liran
11 Pestov, Vladimir G.
10 Funano, Kei
10 Huang, Qingzhong
10 Johnson, William Buhmann
10 Li, Aijun
10 Odell, Edward
10 Rudelson, Mark
10 Schlumprecht, Thomas
10 Schütt, Carsten
10 Xiong, Ge
9 Bastero, Jesús
9 Koldobsky, Alexander L.
9 Pivovarov, Peter
9 Slomka, Boaz A.
9 Thäle, Christoph
9 Valettas, Petros
8 Barthe, Franck
8 Böröczky, Karoly jun.
8 Brazitikos, Silouanos
8 Leng, Gangsong
8 Mohar, Bojan
8 Temlyakov, Vladimir Nikolaevich
8 Tikhomirov, Konstantin E.
8 Tsolomitis, Antonis
8 Villa, Rafael
8 Ye, Deping
8 Zhang, Gaoyong
7 Argyros, Spiros A.
7 Aubrun, Guillaume
7 Ball, Keith Martin
7 Carl, Bernd
7 Colesanti, Andrea
7 Gordon, Yehoram
7 He, Binwu
7 Jiménez, Carlos Hugo
7 Ledoux, Michel
7 Lee, James R.
7 Matoušek, Jiří
7 Merino, Bernardo González
7 Pisier, Gilles
7 Schmuckenschläger, Michael
6 Bollobás, Béla
6 Dilworth, Stephen J.
6 Friedland, Omer
6 Gluskin, Efim D.
6 Kabluchko, Zakhar A.
6 Kerr, David
6 Li, Hanfeng
6 Liu, Shiping
6 Lutwak, Erwin
6 Madiman, Mokshay M.
6 Naszódi, Márton
6 Peres, Yuval
6 Sodin, Sasha
6 Yang, Deane
5 Adamczak, Radosław
5 Bernués, Julio
5 Boche, Holger
5 Castillo, Jesús M. F.
5 Chasapis, Giorgos
5 Cordero-Erausquin, Dario
5 Dafnis, Nikos
5 Dehici, Abdelkader
5 Figiel, Tadeusz
5 Goldreich, Oded
5 Gozlan, Nathael
5 Huang, Han
5 Jeribi, Aref
5 Lindenstrauss, Joram
5 Linial, Nathan
5 Lubetzky, Eyal
...and 1,403 more Authors
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Cited in 297 Serials

121 Israel Journal of Mathematics
98 Journal of Functional Analysis
81 Advances in Mathematics
64 Proceedings of the American Mathematical Society
57 Journal of Mathematical Analysis and Applications
36 Discrete & Computational Geometry
33 Transactions of the American Mathematical Society
24 The Annals of Probability
24 Geometric and Functional Analysis. GAFA
20 Geometriae Dedicata
19 Discrete Mathematics
19 Probability Theory and Related Fields
19 Linear Algebra and its Applications
18 Communications in Mathematical Physics
18 Communications in Contemporary Mathematics
18 Comptes Rendus. Mathématique. Académie des Sciences, Paris
17 Inventiones Mathematicae
17 Mathematika
16 Applied Mathematics and Computation
15 Advances in Applied Mathematics
15 Combinatorica
15 The Journal of Geometric Analysis
14 Compositio Mathematica
14 Duke Mathematical Journal
13 Archiv der Mathematik
13 Mathematische Annalen
13 Journal of Theoretical Probability
12 European Journal of Combinatorics
12 Bulletin of the American Mathematical Society. New Series
12 Positivity
11 Combinatorics, Probability and Computing
11 Advances in Geometry
10 Journal of Mathematical Physics
10 Journal of Approximation Theory
10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
10 Journal of Complexity
9 Studia Mathematica
9 Acta Mathematica
9 Journal of Combinatorial Theory. Series A
9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
9 Calculus of Variations and Partial Differential Equations
9 Journal of the European Mathematical Society (JEMS)
8 Discrete Applied Mathematics
8 Constructive Approximation
8 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
8 Journal of Mathematical Sciences (New York)
8 Journal of Inequalities and Applications
7 Information Processing Letters
7 Mathematical Notes
7 Mathematical Proceedings of the Cambridge Philosophical Society
7 Functional Analysis and its Applications
7 Mathematische Zeitschrift
7 Monatshefte für Mathematik
7 Graphs and Combinatorics
7 Journal of the American Mathematical Society
7 St. Petersburg Mathematical Journal
6 Annales de l’Institut Fourier
6 Manuscripta Mathematica
6 Bernoulli
6 Geometry & Topology
6 Nonlinear Analysis. Real World Applications
5 Computers & Mathematics with Applications
5 Journal of Combinatorial Theory. Series B
5 Journal of Computational and Applied Mathematics
5 Journal of Soviet Mathematics
5 Theoretical Computer Science
5 Applied and Computational Harmonic Analysis
5 Acta Mathematica Sinica. English Series
4 Automatica
4 Journal of the Mathematical Society of Japan
4 Mathematische Nachrichten
4 Quaestiones Mathematicae
4 Results in Mathematics
4 Topology and its Applications
4 Statistics & Probability Letters
4 Annals of Pure and Applied Logic
4 Algorithmica
4 Applied Mathematics Letters
4 SIAM Journal on Discrete Mathematics
4 Random Structures & Algorithms
4 The Annals of Applied Probability
4 Designs, Codes and Cryptography
4 Stochastic Processes and their Applications
4 Mathematical Programming. Series A. Series B
4 The Electronic Journal of Combinatorics
4 Electronic Journal of Probability
4 The Journal of Fourier Analysis and Applications
4 Journal of Topology and Analysis
4 Journal of Function Spaces
4 Nonlinear Analysis. Theory, Methods & Applications
3 Archive for Rational Mechanics and Analysis
3 Journal d’Analyse Mathématique
3 Journal of Statistical Physics
3 Theory of Probability and its Applications
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 The Annals of Statistics
3 Calcolo
3 Publications Mathématiques
3 Integral Equations and Operator Theory
3 Journal of Computer and System Sciences
...and 197 more Serials
all top 5

Cited in 54 Fields

518 Convex and discrete geometry (52-XX)
478 Functional analysis (46-XX)
299 Probability theory and stochastic processes (60-XX)
246 Combinatorics (05-XX)
124 Operator theory (47-XX)
94 Differential geometry (53-XX)
83 Real functions (26-XX)
80 Computer science (68-XX)
75 Ordinary differential equations (34-XX)
56 Information and communication theory, circuits (94-XX)
55 Linear and multilinear algebra; matrix theory (15-XX)
48 Measure and integration (28-XX)
43 Dynamical systems and ergodic theory (37-XX)
43 General topology (54-XX)
38 Approximations and expansions (41-XX)
38 Harmonic analysis on Euclidean spaces (42-XX)
38 Calculus of variations and optimal control; optimization (49-XX)
37 Partial differential equations (35-XX)
36 Quantum theory (81-XX)
36 Operations research, mathematical programming (90-XX)
35 Abstract harmonic analysis (43-XX)
35 Statistics (62-XX)
33 Numerical analysis (65-XX)
32 Topological groups, Lie groups (22-XX)
32 Global analysis, analysis on manifolds (58-XX)
30 Geometry (51-XX)
29 Group theory and generalizations (20-XX)
29 Difference and functional equations (39-XX)
27 Number theory (11-XX)
22 Mathematical logic and foundations (03-XX)
20 Statistical mechanics, structure of matter (82-XX)
17 Manifolds and cell complexes (57-XX)
16 Several complex variables and analytic spaces (32-XX)
15 Functions of a complex variable (30-XX)
13 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
13 Biology and other natural sciences (92-XX)
12 Order, lattices, ordered algebraic structures (06-XX)
12 Algebraic topology (55-XX)
10 Algebraic geometry (14-XX)
10 Systems theory; control (93-XX)
9 Integral transforms, operational calculus (44-XX)
7 General and overarching topics; collections (00-XX)
6 History and biography (01-XX)
5 Integral equations (45-XX)
3 Field theory and polynomials (12-XX)
3 Potential theory (31-XX)
3 Mechanics of particles and systems (70-XX)
2 Nonassociative rings and algebras (17-XX)
2 Special functions (33-XX)
2 Sequences, series, summability (40-XX)
2 Mechanics of deformable solids (74-XX)
1 Commutative algebra (13-XX)
1 Fluid mechanics (76-XX)
1 Classical thermodynamics, heat transfer (80-XX)

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