This is an announcement for the paper "Modified Busemann-Petty problem on sections of convex bodies" by A.Koldobsky, V.Yaskin and M.Yaskina.

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 is affirmative if $n\le 4$ and negative if $n\ge 5$. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.

Archive classification: Functional Analysis

Mathematics Subject Classification: 52Axx

Remarks: 17 pages

The source file(s), modBP.tex: 33931 bytes, is(are) stored in gzipped form as 0410496.gz with size 10kb. The corresponding postcript file has gzipped size 64kb.

Submitted from: yaskinv@math.missouri.edu

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