This is an announcement for the paper "A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space" by V.Yaskin.
Abstract: 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 $\mathbb{H}^n$.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 52A55, 52A20, 46B20
Remarks: 12 pages, 2 figures
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Submitted from: yaskinv@math.missouri.edu
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