$L_p$ Radial Minkowski Homomorphisms
$L_p$ Radial Minkowski Homomorphisms
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DOI：
10.11650/tjm.15.2011.50
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发表时间：
2011-01
影响因子：
0.4
通讯作者：
Wei Wang;Lijuan Liu;Binwu He
中科院分区：
文献类型：
--
作者：
Wei Wang;Lijuan Liu;Binwu He
相交体定义了连续的$GL（n）$逆变赋值，它在Busemann-Petty问题的解决中发挥着至关重要的作用。本文引入了$L_{p}$径向Minkowski同态的概念，并考虑了Busemann-Petty型问题$\Phi_{p} K\subseteq \Phi_{p} L$是否蕴涵$V（K）\leq V（L）$，其中$\Phi_{p}$是星星体上的一个$\displaystyle\left（\frac{n}{p}-1\right）$次齐次连续算子，它是一个$SO（n）$等变赋值. Schuster的结果被推广到一个大类的$L_{p}$径向赋值。
Intersection bodies define a continuous and $GL(n)$ contravariant valuation which plays a crucial role in the solution of the Busemann-Petty problem. In this paper, we introduce the concept of $L_{p}$ radial Minkowski homomorphisms and consider the Busemann-Petty type problem whether $\Phi_{p} K\subseteq \Phi_{p} L$ implies $V(K)\leq V(L)$, where $\Phi_{p}$ is a homogeneous of degree $\displaystyle\left(\frac{n}{p}-1\right)$, continuous operator on star bodies which is an $SO(n)$ equivariant valuation. Previous results by Schuster are generalized to a large class of $L_{p}$ radial valuations.