Vitali Milman | Academic Influence

Vitali Milman's AcademicInfluence.com Rankings

Vitali Milman

Mathematics

#618

World Rank

#1152

Historical Rank

Functional Analysis

#12

World Rank

#20

Historical Rank

Measure Theory

#297

World Rank

#458

Historical Rank

mathematics Degrees

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Mathematics

Vitali Milman's Degrees

PhD Mathematics Moscow State University

Why Is Vitali Milman Influential?

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According to Wikipedia, Vitali Davidovich Milman is a mathematician specializing in analysis. He is a professor at the Tel Aviv University. In the past he was a President of the Israel Mathematical Union and a member of the “Aliyah” committee of Tel Aviv University.

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Vitali Milman's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

lambda1, Isoperimetric inequalities for graphs, and superconcentrators (1985) (572)
il , , lsoperimetric Inequalities for Graphs , and Superconcentrators (1985) (568)
Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space (1989) (474)
New volume ratio properties for convex symmetric bodies in ℝn (1987) (332)
Approximation of zonoids by zonotopes (1989) (235)
Asymptotic Geometric Analysis, Part I (2015) (223)
The Santalo point of a function, and a functional form of the Santalo inequality (2004) (168)
Geometry of Log-concave Functions and Measures (2005) (147)
Extremal problems and isotropic positions of convex bodies (2000) (111)
Entropy and Asymptotic Geometry of Non-Symmetric Convex Bodies☆ (2000) (109)
On type of metric spaces (1986) (109)
Functional analysis : an introduction (2004) (106)
The concept of duality in convex analysis, and the characterization of the Legendre transform (2009) (104)
Geometric Aspects of Functional Analysis (2020) (91)
Asymptotic Infinite-Dimensional Theory of Banach Spaces (1994) (90)
Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space (1985) (82)
Concentration Property on Probability Spaces (2000) (81)
Averages of norms and quasi-norms (1998) (81)
Chapter 17 - Euclidean Structure in Finite Dimensional Normed Spaces (2001) (78)
The Local Theory of Normed Spaces and its Applications to Convexity (1993) (66)
Better Expanders and Superconcentrators (1987) (65)
Isomorphic symmetrization and geometric inequalities (1988) (64)
Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality (1985) (62)
Minkowski sums and symmetrizations (1988) (57)
Unconditional and symmetric sets inn-dimensional normed spaces (1980) (57)
Duality of metric entropy (2004) (55)
Coordinate density of sets of vectors (1978) (51)
Hidden structures in the class of convex functions and a new duality transform (2011) (51)
The "M"-ellipsoid, symplectic capacities and volume (2006) (48)
The concept of duality for measure projections of convex bodies (2008) (48)
Symmetrization and Isotropic Constants of Convex Bodies (2004) (46)
Estimates related to steiner symmetrizations (1989) (42)
A few observations on the connections between local theory and some other fields (1988) (41)
Asymptotic $l_p$ spaces and bounded distortions (1992) (41)
Mixed integrals and related inequalities (2012) (41)
Convex bodies with minimal mean width (2000) (41)
Dvoretzky's theorem — Thirty years later (1992) (40)
A Remarkable Measure Preserving Diffeomorphism between two Convex Bodies in ℝn (1999) (39)
Topics in Asymptotic Geometric Analysis (2000) (39)
Asymptotic Convex Geometry Short Overview (2004) (38)
The distance between certainn-dimensional Banach spaces (1981) (38)
On the covering numbers of convex bodies (1987) (33)
MEAN WIDTH AND DIAMETER OF PROPORTIONAL SECTIONS OF A SYMMETRIC CONVEX BODY (1998) (33)
Isomorphic Steiner symmetrization (2003) (31)
Institute for Mathematical Physics Euclidean Structure in Finite Dimensional Normed Spaces Euclidean Structure in Finite Dimensional Normed Spaces (2009) (30)
On the diameter of proportional sections of a symmetric convex body (1997) (29)
Asymptotic formulas for the diameter of sections of symmetric convex bodies (2005) (28)
Geometrization of Probability (2007) (28)
Some applications of duality relations (1991) (25)
Regularization of star bodies by random hyperplane cut off (2003) (24)
Characterizing the derivative and the entropy function by the Leibniz rule (2011) (24)
Minkowski spaces with extremal distance from the Euclidean space (1978) (24)
THE COVERING NUMBERS AND LOW M*-ESTIMATE FOR QUASI-CONVEX BODIES (1996) (23)
Distances between normed spaces, their subspaces and quotient spaces (1986) (23)
Logarithmic reduction of the level of randomness in some probabilistic geometric constructions (2006) (23)
A characterization of the support map (2010) (22)
On a geometric inequality (1988) (22)
A geometric lemma and duality of entropy numbers (2000) (21)
A characterization of product preserving maps with applications to a characterization of the Fourier transform (2010) (21)
The chain rule as a functional equation (2010) (21)
The concept of duality in convex analysis (2016) (20)
Geometric aspects of functional analysis : Israel Seminar (GAFA), 1987-88 (1989) (20)
Surprising Geometric Phenomena in High-Dimensional Convexity Theory (1998) (18)
Rapid Steiner Symmetrization of Most of a Convex Body and the Slicing Problem (2005) (18)
A characterization of the Fourier transform and related topics (2008) (18)
Geometric Probability and Random Cotype 2 (2004) (18)
Convex Geometric Analysis (1998) (17)
Order Isomorphisms on Convex Functions in Windows (2015) (17)
Note on the Geometric-Arithmetic Mean Inequality (2003) (15)
$\alpha$-concave functions and a functional extension of mixed volumes (2013) (15)
Volume approach and iteration procedures in local theory of normed spaces (1985) (15)
On Convexified Packing and Entropy Duality (2004) (15)
A reduction of the slicing problem to finite volume ratio bodies (2003) (14)
Diameter of a minimal invariant subset of equivariant lipschitz actions on compact subsets of ℝ k (1987) (14)
Polynomial bounds for Large Bernoulli sections of ℓ1N (2006) (12)
ON MILMAN ’ S ELLIPSOIDS AND M – POSITION OF CONVEX BODIES (2010) (12)
A new proof of the Maurey-Pisier theorem (1979) (11)
Non-standard Constructions in Convex Geometry: Geometric Means of Convex Bodies (2017) (11)
Entropy methods in asymptotic convex geometry (1999) (11)
On Multiplicative Maps of Continuous and Smooth Functions (2011) (10)
Geometric applications of Chernoff-type estimates and a ZigZag approximation for balls (2005) (10)
An Operator Equation Generalizing the Leibniz Rule for the Second Derivative (2012) (9)
How small can the intersection of a few rotations of a symmetric convex body be (1997) (9)
Characterizing addition of convex sets by polynomiality of volume and by the homothety operation (2015) (8)
Geometric Applications of Chernoff-Type Estimates (2007) (8)
More on the duality conjecture for entropy numbers (2003) (8)
Randomizing properties of convex high-dimensional bodies and some geometric inequalities (2002) (8)
Characterizing the mixed volume (2011) (7)
Duality of metric entropy in Euclidean space (2003) (7)
Geometrical Aspects of Functional Analysis: Israel Seminar, 1985-86 (1987) (7)
Some Remarks on a Lemma of Ran Raz (2003) (7)
The Concentration Phenomenon and Linear Structure of Finite-Dimensional Normed Spaces (2010) (7)
A new duality transform (2008) (7)
A geometric approach to duality of metric entropy (2001) (7)
The Concentration Phenomenon and Linear Structure of Finite-Dimensional Normed Spaces (2010) (7)
Weighted geometric means of convex bodies (2019) (6)
On subspaces contained in subsets of finite homogeneous spaces (1978) (6)
Rigidity and stability of the Leibniz and the chain rule (2013) (6)
Stability of the Blaschke–Santaló and the affine isoperimetric inequality (2010) (6)
Some remarks about embeddings ofl1k in finite-dimensional spaces (1982) (6)
Some remarks on Urysohn's inequality and volume ratio of cotype 2-spaces (1987) (5)
Order isomorphisms in windows (2011) (5)
On the Euclidean Metric Entropy of Convex Bodies (2007) (5)
A characterization of duality through section/projection correspondence in the finite dimensional setting☆ (2011) (5)
An operator equation characterizing the Laplacian (2013) (5)
Reciprocals and Flowers in Convexity (2018) (5)
A characterization of the mixed discriminant (2013) (5)
A functional equation characterizing the second derivative (2011) (5)
Powers and logarithms of convex bodies (2017) (4)
The slicing problem by Bourgain (2020) (4)
Asymptotic geometric analysis : proceedings of the fall 2010 Fields Institute thematic program (2013) (4)
The derivation equation for Ck-functions: stability and localization (2014) (4)
Essentially-Euclidean convex bodies (2010) (4)
Asymptotic Geometric Analysis, Part II (2021) (4)
On the Oscillation Rigidity of a Lipschitz Function on a High-Dimensional Flat Torus (2014) (4)
Averages of norms and behavior of families of projective caps on the sphere (1997) (4)
Operator Functional Equations in Analysis (2013) (4)
Stability results for some classical convexity operations (2013) (4)
Polynomial bounds for large Bernoulli sections of $\ell_1^N$ (2006) (4)
Stabilized asymptotic structures and envelopes in banach spaces (2000) (3)
USING RADEMACHER PERMUTATIONS TO REDUCE RANDOMNESS (2007) (3)
The chain rule functional equation on Rn (2011) (3)
LowM*-Estimates on Coordinate Subspaces☆ (1996) (3)
Phenomena arising from high dimensionality (2004) (3)
Operator Relations Characterizing Derivatives (2018) (3)
When random proportional subspaces are also random quotients (2004) (3)
Novel View on Classical Convexity Theory (2020) (3)
“Irrational” constructions in Convex Geometry (2017) (3)
Entropy extension (2006) (2)
Sudakov type inequalities for convex bodies in IR n (1987) (2)
The Leibniz Rule (2018) (2)
Isomorphic Random Subspaces and Quotients of Convex and Quasi-Convex Bodies (2004) (2)
Operator equations and domain dependence, the case of the Schwarzian derivative (2014) (1)
Essential Uniqueness of an M-Ellipsoid of a Given Convex Body (2004) (1)
Orbit Point of View on Some Results of Asymptotic Theory; Orbit Type and Cotype (2017) (1)
Submultiplicative functions and operator inequalities (2014) (1)
Entropy Numbers and Duality for Operators with Values in a Hilbert Space (1990) (1)
SG ] 4 J un 2 00 6 The M-ellipsoid , Symplectic Capacities and Volume (2019) (0)
Simplicity v/s Complexity in the Framework of Geometric Asymptotic Analysis and Some New Applications of the Concentration Phenomenon (2006) (0)
Unbounded self-adjoint and symmetric operators in (2004) (0)
Liran Rotem – Publication List (2017) (0)
Characterizing summations of convex sets (2014) (0)
Linear spaces; normed spaces; first examples (2004) (0)
Asymptoti Convex Geometry : a shortoverviewA (2014) (0)
Non-localization Results (2018) (0)
Characterizing the Radial Sum for Star Bodies (2017) (0)
The derivation equation for Ck-functions: stability and localization (2014) (0)
Derivative and entropy: the only derivations from $C^1(RR)$ to $C(RR)$ (2011) (0)
Self-adjoint operators (2004) (0)
Regular Solutions of Some Functional Equations (2018) (0)
The Chain Rule Inequality and its Perturbations (2018) (0)
Ju l 2 00 4 Duality of Metric Entropy ∗ (2004) (0)
Rigidity of the Chain Rule and Nearly Submultiplicative Functions (2017) (0)
Addendum: Discussions at the Dead Sea (2000) (0)
Submultiplicative Operators on C k -Spaces (2018) (0)
Classical positions of convex bodies (2015) (0)
Rigidity and stability of the Leibniz and the chain rule (2013) (0)
Convex bodies with minimal mean widthA (2014) (0)
Appendix. Solutions to exercises (2004) (0)
The fundamental theorems and the basic methods (2004) (0)
Bounded linear operators (2004) (0)
Ju l 2 00 4 On convexified packing and entropy duality (2004) (0)
The dual space (2004) (0)
From Functional Analysis to Asymptotic Geometric Analysis (2004) (0)
Joran Lindenstrauss, in Memoriam (2015) (0)
Geometries in Interaction (1995) (0)
Aleksander (Olek) Pelczynski (1932–2012) (2017) (0)
Essentially-Euclidean convex bodies 1 (2010) (0)
Functions of operators; spectral decomposition (2004) (0)
Convex bodies: Classical geometric inequalities (2015) (0)
Isomorphic isoperimetric inequalities and concentration of measure (2015) (0)
The Second-Order Chain Rule (2018) (0)
-position and the reverse Brunn-Minkowski inequality (2015) (0)
Almost Euclidean subspaces of finite dimensional normed spaces (2015) (0)
ASYMPTOTIC GEOMETRY OF RANDOM POLYTOPES (2019) (0)
The Chain Rule Operator Equation for Polynomials and Entire Functions (2017) (0)
Book Review: Convex bodies\RM : The Brunn-Minkowski theory (1995) (0)
How small an the interse tion of a fewrotations of a symmetri onvex body be ? (2014) (0)
Spectrum. Fredholm theory of compact operators (2004) (0)
Metric entropy and covering numbers estimates (2015) (0)
Volume distribution in convex bodies (2015) (0)
On the diameter of proportional se tionsof a symmetri onvex bodyA (2014) (0)
Identifying Set Inclusion by Projective Positions and Mixed Volumes (2015) (0)
Functional Analysis / Geometry Duality of metric entropy in Euclidean space (2003) (0)
The Chain Rule (2018) (0)
Spectral theory of unitary operators (2004) (0)
Extremal problems and isotropi positionsof onvex bodiesA (2014) (0)
Stability and Rigidity of the Leibniz and the Chain Rules (2018) (0)
Functional Analysis/Geometry A new duality transform ✩ (2008) (0)
The ℓ-position and the Rademacher projection (2015) (0)
QUASI-CONVEX BODIES (1998) (0)
Approximation of zonoids by zonotopes ( 1 ) (2006) (0)
The Second-Order Leibniz rule (2018) (0)
The Extended Leibniz Rule and Related Equations in the Space of Rapidly Decreasing Functions (2018) (0)

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