English

The complex Busemann-Petty problem on sections of convex bodies

Functional Analysis 2007-07-27 v1 Metric Geometry

Abstract

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in \Cn\C^n with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if n3n\le 3 and negative if n4.n\ge 4.

Keywords

Cite

@article{arxiv.0707.3851,
  title  = {The complex Busemann-Petty problem on sections of convex bodies},
  author = {A. Koldobsky and H. König and M. Zymonopoulou},
  journal= {arXiv preprint arXiv:0707.3851},
  year   = {2007}
}

Comments

18 pages

R2 v1 2026-06-21T09:01:55.203Z