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

2008/07/04 by Marisa Zymonopoulou, Zymonopoulou, Marisa · 1 citation
Mathematics · #Morphological variations and asymmetry #Point processes and geometric inequalities #math.FA

paper · pdf · doi:10.48550/arxiv.0807.0776

arxiv created 2008/07/04 · arxiv updated 2009/12/01

Abstract

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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• Comparison of volumes of convex bodies in real, complex, and quaternionic spaces

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