Busemann's intersection inequality in hyperbolic and spherical spaces

Abstract

Busemann's intersection inequality asserts that the only maximizers of the integral integral(sn-1) |K boolean AND xi(perpendicular to)| (n) d xi 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. (C) 2018 Elsevier Inc. All rights reserved.