The Lower Dimensional Busemann-Petty Problem in the Complex Hyperbolic Space
Functional Analysis
2017-05-17 v2
Abstract
The lower dimensional Busemann-Petty problem asks whether origin-symmetric convex bodies in R^n with smaller volume of all k-dimensional sections necessarily have smaller volume. The answer is negative for k>3. The problem is still open for k=2,3. We study this problem in the complex hyperbolic n-space and prove that the answer is affirmative only for sections of complex dimension one and negative for sections of higher dimensions.
Cite
@article{arxiv.1307.7420,
title = {The Lower Dimensional Busemann-Petty Problem in the Complex Hyperbolic Space},
author = {Susanna Dann},
journal= {arXiv preprint arXiv:1307.7420},
year = {2017}
}
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