On sections of convex bodies in hyperbolic space

被引：2

作者：

Hiripitiyage, K. L. H. ^{[1
]}

Yaskin, V. ^{[1
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 445卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Convex body; Origin-symmetric body; Hyperbolic space; Fourier transform; BUSEMANN-PETTY PROBLEM;

D O I：

10.1016/j.jmaa.2016.07.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider two problems on sections of convex bodies in hyperbolic space. The first one is a modified version of the Busemann Petty problem. We look at conditions that guarantee a positive answer to this problem in all dimensions. The second problem is an analogue of a result of Makai, Martini, and Odor about origin symmetry. If in every direction the parallel section function has a critical value at zero, then the body is origin-symmetric. For both problems we use Fourier transform techniques. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1394 / 1409

页数：16

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