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The Busemann-Petty problem in hyperbolic and spherical spaces

V. Yaskin
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Abstract

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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V. Yaskin. 2004-10-22. The Busemann-Petty problem in hyperbolic and spherical spaces. https://arxiv.org/abs/math/0410501

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