In addition, the sharp upper bound of the minimal p-mean width ofLp zonoids is obtained

The idea is to approximate the infinite dimensional problem by a finite dimensional one, to show convexity of the minimizers of the finite dimensional problems and prove convergence

The sharp bounds for the affine invariant ratio of the mixed cone-volume functional to the Minkowski first mixed volume are obtained, and therefore new affine isoperimetric inequalities

(Böröczky-Lutwak-Yang-Zhang, [4]) A non-zero finite even Borel measure on the unit sphere S n−1 is the cone-volume measure of an origin-symmetric convex body in R n if and only if

We calculate the upper transform C 2,λ u (f ) for non- smooth convex functions arising from convex programming, such as the maximum function (1.8), and we also use an anisotropic

This was first proved by Comets and Yoshida [3, Theorem 2.4.4], for a model of directed polymers in which the random walk is replaced by a Brownian motion and the environment is

and its generalizations when all the variables are positive definite, bounded, self- adjoint linear operators on a Hilbert space... For example, a very special case

Pinelis, Birkh¨ auser, Basel L’Hospital type rules for monotonicity: applications to probability inequalities for sums of bounded random variables. Pinelis, Binomial upper bounds

This motivates Section 3, where only the substrate is random, and the film is defined as the infimum of a collection of Wulff shapes over the substrate.. In Section 4 we prove