This is an announcement for the paper "The complex Busemann-Petty problem on sections of convex bodies" by A.Koldobsky, H.Koenig, and M.Zymonopoulou.

Abstract: The complex Busemann-Petty problem asks whether origin symmetric convex bodies in $\C^n$ with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if $n\le 3$ and negative if $n\ge 4.$

Archive classification: math.FA math.MG

Mathematics Subject Classification: 52A20

Remarks: 18 pages

The source file(s), complexbp.tex: 46749 bytes, is(are) stored in gzipped form as 0707.3851.gz with size 14kb. The corresponding postcript file has gzipped size 101kb.

Submitted from: koldobsk@math.missouri.edu

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