The Busemann-Petty Problem in Complex Hyperbolic Space
Classical Analysis and ODEs
2012-09-07 v2
Abstract
The Busemann-Petty problem asks whether origin-symmetric convex bodies in real Euclidean n-space with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative for n less or equal to 4 and negative if n greater or equal to 5. We study this problem in the complex hyperbolic n-space and prove that the answer is affirmative for n less or equal to 2 and negative for n greater or equal to 3.
Cite
@article{arxiv.1112.2192,
title = {The Busemann-Petty Problem in Complex Hyperbolic Space},
author = {Susanna Dann},
journal= {arXiv preprint arXiv:1112.2192},
year = {2012}
}
Comments
19 pages