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arXiv · 1307.7420

The Lower Dimensional Busemann-Petty Problem in the Complex Hyperbolic Space

Susanna Dann
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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.

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Susanna Dann. 2015-01-13. The Lower Dimensional Busemann-Petty Problem in the Complex Hyperbolic Space. https://doi.org/10.1017/s0305004113000054

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