Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624788 | Advances in Applied Mathematics | 2014 | 17 Pages |
Abstract
The lower dimensional Busemann–Petty problem asks whether origin-symmetric convex bodies in RnRn with smaller volume of all k -dimensional sections necessarily have smaller volume. The answer is negative for k>3k>3. The problem is still open for k=2,3k=2,3. We study this problem in the complex hyperbolic n -space HCn and prove that the answer is affirmative only for sections of complex dimension one and negative for sections of higher dimensions.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Susanna Dann,