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Modified Busemann-Petty problem on sections of convex bodies

A. Koldobsky·V. Yaskin·M. Yaskina
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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 is affirmative if $n\le 4$ and negative if $n\ge 5$. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.

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A. Koldobsky, V. Yaskin, M. Yaskina. 2004-10-22. Modified Busemann-Petty problem on sections of convex bodies. https://arxiv.org/abs/math/0410496

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