The Busemann-Petty problem in hyperbolic and spherical spaces

The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer to this problem is affirmative if $n\le 4$ and negative if $n\ge 5$. We study this problem in hyperbolic and spherical spaces.Comment: 16 pages, 2 figure

Inequalities of the Kahane–Khinchin type and sections of L p

International audienceWe extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in L-p, p, > -2

A generalization of the Busemann-Petty problem on sections of convex bodies

address