Busemann's intersection inequality in hyperbolic and spherical spaces

Busemann's intersection inequality asserts that the only maximizers of the integral ∫Sn−1|K∩ξ⊥|ndξ among all convex bodies of a fixed volume in Rn are centered ellipsoids. We study this question in the hyperbolic and spherical spaces, as well as general measure spaces.

Saved in:
Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2018-02, Vol.326, p.521-560
Main Authors: Dann, Susanna, Kim, Jaegil, Yaskin, Vladyslav
Format: Article
Language:English
Subjects:
Convex bodies
Hyperbolic and spherical spaces
Radon transform
Sections
Spherical harmonics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Busemann's intersection inequality asserts that the only maximizers of the integral ∫Sn−1|K∩ξ⊥|ndξ among all convex bodies of a fixed volume in Rn are centered ellipsoids. We study this question in the hyperbolic and spherical spaces, as well as general measure spaces.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2018.01.008