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arXiv · 0707.3851

The complex Busemann-Petty problem on sections of convex bodies

A. Koldobsky·H. König·M. Zymonopoulou
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Abstract

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in $\C^n$ with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if $n\le 3$ and negative if $n\ge 4.$

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A. Koldobsky, H. König, M. Zymonopoulou. 2007-07-26. The complex Busemann-Petty problem on sections of convex bodies. https://arxiv.org/abs/0707.3851

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