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

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dc.creatorYaskin, V.
dc.date2005-03-15
dc.date.accessioned2026-07-07T05:17:57Z
dc.date.available2026-07-07T05:17:57Z
dc.descriptionThe 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 $\mathbb{H}^n$.
dc.description12 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0503289
dc.identifierhttp://arxiv.org/abs/math/0503289
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74495
dc.subjectFunctional Analysis
dc.subjectMetric Geometry
dc.subject52A55, 52A20, 46B20
dc.titleA solution to the lower dimensional Busemann-Petty problem in the hyperbolic space
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