Modified Busemann-Petty problem on sections of convex bodies

Details Modified Busemann-Petty problem on sections of convex bodies Modified Busemann-Petty problem on sections of convex bodies

2004-10-22

arxiv.org/abs/math/0410496v1

Mathematics

Functional Analysis

17 pages

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 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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