A multivariate Berry-Esseen theorem with explicit constants Page 1 Bernoulli 25(4A), 2019,
2824–2853 https://doi.org/10.3150/18-BEJ1072 A multivariate Berry–Esseen theorem with …

The inequalities of Petty and Zhang are affine isoperimetric‐type inequalities providing
sharp bounds for Vol nn− 1 (K) Vol n (Π∘ K) \rmVol^n-1_n(K)\rmVol_n(Π^∘K), where Π K …

Abstract The Brunn-Minkowski theory in convex geometry concerns, among other things, the
volumes, mixed volumes, and surface area measures of convex bodies. We study …

On the stability of Brunn–Minkowski type inequalities - ScienceDirect Skip to main contentSkip
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Minkowski's Theorem asserts that every centered measure on the sphere which is not
concentrated on a great subsphere is the surface area measure of some convex body, and …

We study several of the recent conjectures in regards to the role of symmetry in the
inequalities of Brunn–Minkowski type, such as the L_p L p-Brunn–Minkowski conjecture of …

We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex
symmetric sets with respect to the Gaussian measure. Namely, letting $ J_ {k-1}(s)=\int^ s_0 …

In this paper we extend the concepts of L p-mixed volumes and L p-surface area measures
to L p-mixed μ-measures and L p-surface μ-area measures, respectively, for a measure μ on …

We show that for any even log-concave probability measure $\mu $ on $\mathbb {R}^ n $,
any pair of symmetric convex sets $ K $ and $ L $, and any $\lambda\in [0, 1] $,\begin …

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 …