The modified complex Busemann-Petty problem on sections of convex bodies
Functional Analysis
2008-07-08 v1
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.
Cite
@article{arxiv.0807.0776,
title = {The modified complex Busemann-Petty problem on sections of convex bodies},
author = {Marisa Zymonopoulou},
journal= {arXiv preprint arXiv:0807.0776},
year = {2008}
}