This is an announcement for the paper "Centroids and comparison of volumes" by V.Yaskin and M.Yaskina.

Abstract: For $-1<p<1$ we introduce the concept of a polar $p$-centroid body ${\Gamma^*_p K}$ of a star body $K$. We consider the question of whether ${\Gamma^*_p K}\subset {\Gamma^*_p L}$ implies $\mathrm{vol}(L)\le \mathrm{vol}(K).$ Our results extend the studies by Lutwak in the case $p=1$ and Grinberg, Zhang in the case $p> 1$.

Archive classification: Functional Analysis

Mathematics Subject Classification: 52Axx

Remarks: 18 pages

The source file(s), centr.tex: 51970 bytes, is(are) stored in gzipped form as 0503290.gz with size 13kb. The corresponding postcript file has gzipped size 71kb.

Submitted from: yaskinv@math.missouri.edu

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