A UNIVERSAL BOUND IN THE DIMENSIONAL BRUNN-MINKOWSKI INEQUALITY FOR LOG-CONCAVE MEASURES

被引：2

作者：

Livshyts, Galyna V. ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 09期

基金：

美国国家科学基金会;

关键词：

Classification; Gaussian measure; Ehrhard inequality; Convex bodies; symmetry; Brunn-Minkowski inequality; Brascamp-Lieb inequality; Poincare inequality; equality case characterization; torsional rigidity; energy minimization; log-concave measures; CENTRAL-LIMIT-THEOREM; MAXIMAL SURFACE-AREA; CONVEX-BODIES; R-N; SECTIONS; POINCARE; RESPECT; SETS;

D O I：

10.1090/tran/8976

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for any even log-concave probability measure mu on R-n, any pair of symmetric convex sets K and L, and any lambda is an element of [0, 1], mu((1-lambda)K +lambda L)(cn) >= (1-lambda)mu(K)(cn) +lambda mu(L)(cn), where c(n) >= n(-4-o(1)). This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Richard J. Gardner and Artem Zvavitch [Tran. Amer. Math. Soc. 362 (2010), pp. 5333-5353]; Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti [J. Funct. Anal. 273 (2017), pp. 1120-1139]). Moreover, our bound improves for various special classes of logconcave measures.

引用

页码：6663 / 6680

页数：18

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