This is an announcement for the paper "The modified complex Busemann-Petty problem on sections of convex bodies" by Marisa Zymonopoulou.

Abstract: Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions.

Archive classification: math.FA

The source file(s), MCBP.tex: 44421 bytes, is(are) stored in gzipped form as 0807.0776.gz with size 12kb. The corresponding postcript file has gzipped size 104kb.

Submitted from: marisa@math.missouri.edu

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http://arXiv.org/abs/0807.0776

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