Article ID Journal Published Year Pages File Type
4624788 Advances in Applied Mathematics 2014 17 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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