This is an announcement for the paper "The Busemann-Petty problem in hyperbolic and spherical spaces" by V.Yaskin.

Abstract: The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer to this problem is affirmative if $n\le 4$ and negative if $n\ge 5$. We study this problem in hyperbolic and spherical spaces.

Archive classification: Functional Analysis

Mathematics Subject Classification: 52Axx

Remarks: 16 pages, 2 figures

The source file(s), HyperbolicBP.tex: 38485 bytes, pic02.eps: 9386 bytes, picForVlad2.eps: 3824 bytes, is(are) stored in gzipped form as 0410501.tar.gz with size 15kb. The corresponding postcript file has gzipped size 68kb.

Submitted from: yaskinv@math.missouri.edu

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