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

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Abstract

The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in ℝn 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 ℍn.

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  1. Department of Mathematics, University of Oklahoma, 73019, Norman, OK

    V. Yaskin

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  1. V. Yaskin
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Correspondence to V. Yaskin.

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Yaskin, V. A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space. J Geom Anal 16, 735–745 (2006). https://doi.org/10.1007/BF02922139

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