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

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

2008-07-04

arxiv.org/abs/0807.0776v1

Mathematics

Functional Analysis

Scientific paper

Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions.

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