Busemann's intersection inequality in hyperbolic and spherical spaces

2017/06/21 by Dann, Susanna, Kim, Jaegil, Yaskin, Vladyslav
#52A20 #52A38 #52A40 #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 52A55

paper · doi:10.48550/arxiv.1706.06776

Abstract

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

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