The Busemann-Petty problem in hyperbolic and spherical spaces

Details The Busemann-Petty problem in hyperbolic and spherical spaces The Busemann-Petty problem in hyperbolic and spherical spaces

2004-10-22

arxiv.org/abs/math/0410501v1

Mathematics

Functional Analysis

16 pages, 2 figures

Scientific paper

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.

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