凸体的p次径向平均体的几个性质

Several Properties of the Radial pth Mean Bodies of Convex Bodies

中文关键词:  $p$次径向平均体  凸体  径向函数.

英文关键词:the radial $p$th mean body  convex body  radial function.

中文摘要:

      本文证明了凸体的$p$次径向平均体的线性不变性和椭球的$p$次径向平均体仍是椭球，并且获得了$p$次径向平均体相应于Blaschke-Santal$\acute{o}$不等式的一个反向不等式.

英文摘要:

      This paper proves that the radial $p$th mean body is invariant under a general linear transformation and that the radial $p$th mean body of an ellipsoid is an ellipsoid. And corresponding to the Blaschke-Santal\'{o} inequality, a reverse inequality for the radial $p$th mean body is given.