A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space

Details A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space

2005-03-15

arxiv.org/abs/math/0503289v1

Mathematics

Functional Analysis

12 pages, 2 figures

Scientific paper

The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in $\mathbb{R}^n$ with smaller volume of all $k$-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this question is negative if $k>3$. The problem is still open for $k=2,3$. In this article we formulate and completely solve the lower dimensional Busemann-Petty problem in the hyperbolic space $\mathbb{H}^n$.

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