The study of high-dimensional convex bodies from a geometric and analytic point of view,
with an emphasis on the dependence of various parameters on the dimension stands at the …

The Lipschitz extension modulus $ e (M) $ of a metric space $ M $ is the infimum over $ L\ge
1$ such that for any Banach space $ Z $ and any $ C\subset M $, any 1-Lipschitz function …

In this note, we study the maximal perimeter of a convex set in ℝ n with respect to various
classes of measures. Firstly, we show that for a probability measure μ on ℝ n, satisfying very …

We prove several estimates for the volume, the mean width, and the value of the Wills
functional of sections of convex bodies in John's position, as well as for their polar bodies …

We provide general inequalities that compare the surface area in to the minimal, average, or
maximal surface area of its hyperplane or lower dimensional projections. We discuss the …

Optimal Sobolev norms under volume preserving affine transformations are considered. It
turns out that this minimal transform is equivalent to the (p, 2) Fisher information matrix …

The average section functional as (K) of a star body in Rn is the average volume of its
central hyperplane sections: as\left (k\right)= S^ n-1\left| K ∩ ξ^\bot\right| d σ\left (ξ\right) as …

The Lipschitz extension modulus e. M/of a metric space M is the infimum over those L 2 Œ1;
1 such that for any Banach space Z and any C Â M, any 1-Lipschitz function f WC! Z can be …

We prove a reverse Petty projection inequality which is satisfied by every convex body K. We
also study given a convex body K estimates for the dimension k such that there exists a k …

We study some classical positions (minimal surface area position, minimal mean width
position, John's position, Löwner's position and the isotropic position) of a centrally …