The complex Busemann-Petty problem on sections of convex bodies

Details The complex Busemann-Petty problem on sections of convex bodies The complex Busemann-Petty problem on sections of convex bodies

2007-07-26

arxiv.org/abs/0707.3851v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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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