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lambda1, Isoperimetric inequalities for graphs, and superconcentrators

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Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space

It is a special pleasure and honor for the first named author to dedicate this paper to the 60th birthdays of two of his outstanding friends — Israel Gohberg and Ilya Piatetski-Shapiro.

The dimension of almost spherical sections of convex bodies

- T. Figiel, J. Lindenstrauss, V. Milman
- Mathematics
- 1 December 1977

© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1975-1976, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les… Expand

Geometry of Log-concave Functions and Measures

- B. Klartag, V. Milman
- Mathematics
- 1 April 2005

We present a view of log-concave measures, which enables one to build an isomorphic theory for high dimensional log-concave measures, analogous to the corresponding theory for convex bodies. Concepts… Expand

New volume ratio properties for convex symmetric bodies in ℝn

- J. Bourgain, V. Milman
- Mathematics
- 1 June 1987

The Santalo point of a function, and a functional form of the Santalo inequality

- S. Artstein-Avidan, B. Klartag, V. Milman
- Mathematics
- 1 December 2004

Let L(f) denote the Legendre transform of a function f : ℝ n → ℝ. A theorem of K. Ball about even functions is generalized, and it is proved that, for any measurable function f ≥ 0, there exists a… Expand

On type of metric spaces

- J. Bourgain, V. Milman, H. Wolfson
- Mathematics
- 1986

Families of finite metric spaces are investigated. A notion of metric type is introduced and it is shown that for Banach spaces it is consistent with the standard notion of type. A theorem parallel… Expand

Approximation of zonoids by zonotopes

- J. Bourgain, J. Lindenstrauss, V. Milman
- Mathematics
- 1 July 1989

On etudie une propriete d'approximation des corps convexes de R n qui sont des limites de sommes de segments

il , , lsoperimetric Inequalities for Graphs , and Superconcentrators

A general method for obtaining asymptotic isoperimetric inequalities for families of graphs is developed. Some of these inequalities have been applied to functional analysis, This method uses the… Expand

On hilbertian subsets of finite metric spaces

- J. Bourgain, T. Figiel, V. Milman
- Mathematics
- 1 June 1986

The following result is proved: For everyε>0 there is aC(ε)>0 such that every finite metric space (X, d) contains a subsetY such that |Y|≧C(ε)log|X| and (Y, dY) embeds (1 +ε)-isomorphically into the… Expand

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