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lambda1, Isoperimetric inequalities for graphs, and superconcentrators
This method uses the second smallest eigenvalue of a certain matrix associated with the graph and it is the discrete version of a method used before for Riemannian manifolds for asymptotic isoperimetric inequalities for families of graphs.
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
© 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…
Geometry of Log-concave Functions and Measures
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…
New volume ratio properties for convex symmetric bodies in ℝn
The Santalo point of a function, and a functional form of the Santalo inequality
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…
On type of metric spaces
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…
Approximation of zonoids by zonotopes
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…
On hilbertian subsets of finite metric spaces
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…