THE VOLUME PRODUCT OF CONVEX BODIES WITH MANY HYPERPLANE SYMMETRIES

被引：0

作者：

Barthe, F. ^{[1
]}

Fradelizi, M. ^{[2
]}

机构：

[1] Univ Toulouse 3, Equipe Stat & Probabil, CNRS, IMT,UMR 5219, F-31062 Toulouse 9, France

[2] Univ Paris Est Marne La Vallee, Lab Anal & Math Appl, UMR 8050, F-77454 Marne La Vallee 2, France

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2013年 / 135卷 / 02期

关键词：

SANTALO INEQUALITY; MAHLER CONJECTURE; LOCAL MINIMALITY; INTEGRALS; ZONOIDS; SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mahler's conjecture predicts a sharp lower bound on the volume of the polar of a convex body in terms of its volume. We confirm the conjecture for convex bodies with many hyperplane symmetries in the following sense: their hyperplanes of symmetries have a one-point intersection. Moreover, we obtain improved sharp lower bounds for classes of convex bodies which are invariant by certain reflection groups, namely direct products of the isometry groups of regular polytopes.

引用

页码：311 / 347

页数：37