Sections of convex bodies with symmetries

被引：1

作者：

Dann, Susanna ^{[1
]}

Zymonopoulou, Marisa ^{[2
]}

机构：

[1] Vienna Univ Technol, Inst Discrete Math & Geometry, A-1040 Vienna, Austria

[2] Univ Athens, Dept Math, Athens 15784, Greece

来源：

ADVANCES IN MATHEMATICS | 2015年 / 271卷

关键词：

Section of convex bodies; Fourier transform; Busemann-Petty problem; Hyperplane inequality; Busemann's theorem; BUSEMANN-PETTY PROBLEM; POSITIVE-DEFINITE DISTRIBUTIONS; INTERSECTION BODIES; L-P; STABILITY; INEQUALITIES; TERMS;

D O I：

10.1016/j.aim.2014.11.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study how certain symmetries of convex bodies affect their geometric properties. In particular, we consider the impact of symmetries generated by the block diagonal subgroup of orthogonal transformations, generalizing complex and quaternionic convex bodies. We conduct a systematic study of sections of bodies with symmetries of this type, with the emphasis on problems of the Busemann-Petty type and hyperplane inequalities. The main role belongs to the class of intersection bodies with symmetries. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：112 / 152

页数：41

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