Extremal slabs in the cube and the Laplace transform

被引：26

作者：

Barthe, F

Koldobsky, A ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Marne la Vallee, CNRS, Equipe Anal & Math Appl, F-77454 Champs Sur Marne 2, Marne La Vallee, France

来源：

ADVANCES IN MATHEMATICS | 2003年 / 174卷 / 01期

基金：

美国国家科学基金会;

关键词：

volume of slab; Laplace transform; log-concave function;

D O I：

10.1016/S0001-8708(02)00055-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the volume of symmetric slabs in the unit cube. We show that, for t<3/4, the slab parallel to a face has the minimal volume among all symmetric slabs with width t. For large width, we prove the asymptotic extremality of the slab orthogonal to the main diagonal. The proof is based on certain concavity properties of the Laplace transform and on several limit theorems from probability: the central limit theorem and classical principles of moderate and large deviations. Finally, we extend some of the results to more general classes of bodies. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：89 / 114

页数：26