arXiv math/05032902005-03-15math.FA

Centroids and comparison of volumes

V. Yaskin, M. Yaskina

备注：: 18 pages

英文摘要：

For $-1<p<1$ we introduce the concept of a polar $p$-centroid body ${Γ^*_p K}$ of a star body $K$. We consider the question of whether ${Γ^*_p K}\subset {Γ^*_p L}$ 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 $p> 1$.

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