CENTERED CONVEX BODIES AND INEQUALITIES FOR CROSS-SECTION MEASURES

被引：1

作者：

Martini, Horst ^{[1
]}

Mustafaev, Zokhrab ^{[2
]}

机构：

[1] Univ Technol Chemnitz, Horst Martini Fac Math, D-09107 Chemnitz, Germany

[2] Univ Houston Clear Lake City, Dept Math, Houston, TX 77058 USA

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2015年 / 18卷 / 02期

关键词：

Affine isoperimetric inequalities; Busemann's intersection inequality; cross-section measures; dual mixed volumes; ellipsoids; intersection body; Minkowski geometry; mixed volumes; Petty's projection inequality; projection body; zonoids;

D O I：

10.7153/mia-18-56

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to establish some new results on cross-section measures of centered convex bodies. More precisely, we show some connections between inequalities referring to cross-section measures and well-known affine isoperimetric inequalities. Based on this, we derive affine inequalities involving also new characterizations of ellipsoids. In addition, related results on three-dimensional zonoids are obtained. Some of our results are also interesting from the viewpoint of the geometry of finite dimensional real Banach spaces.

引用

页码：759 / 767

页数：9

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