English

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.

Keywords

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}
}
R2 v1 2026-06-21T10:57:35.336Z