Duality of Floating and Illumination Bodies

被引：0

作者：

Mordhorst, Olaf ^{[1
]}

Werner, Elisabeth M. ^{[2
,3
]}

机构：

[1] Tech Univ Wien, Inst Diskrete Math & Geometrie, A-1040 Vienna, Austria

[2] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA

[3] Univ Lille, UFR Math, F-59655 Villeneuve Dascq, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2020年 / 69卷 / 05期

基金：

美国国家科学基金会;

关键词：

Floating bodies; illumination bodies; AFFINE SURFACE; CONVEX-BODIES; RANDOM POLYTOPES; BOUNDARY; APPROXIMATION; REGULARITY; NUMBER; BODY;

D O I：

10.1512/iumj.2020.69.7973

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question for the class of centrally symmetric convex bodies. We provide precise estimates for B-p(n) and for centrally symmetric convex bodies with everywhere positive Gauss curvature. Our estimates show that equality of the polar of the floating body and the illumination body of the polar can only be achieved in the case of ellipsoids.

引用

页码：1507 / 1541

页数：35

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