Busemann's intersection inequality in hyperbolic and spherical spaces

Abstract

Busemann's intersection inequality asserts that the only maximizers of the integral ${\int }_{S^{n-1}}|K\cap {\xi }^{\perp }{|}^{n}d\xi$ among all convex bodies of a fixed volume in ${\mathbb{R}}^n$ are centered ellipsoids. We study this question in the hyperbolic and spherical spaces, as well as general measure spaces.

35 pages, 6 figures