The Orlicz Brunn–Minkowski inequality
The Orlicz Brunn–Minkowski inequality
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DOI：
10.1016/j.aim.2014.02.036
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发表时间：
2014-08
影响因子：
1.7
通讯作者：
Dongmeng Xi;HaiLin Jin;G. Leng
中科院分区：
文献类型：
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作者：
Dongmeng Xi;HaiLin Jin;G. Leng
Orlicz Brunn-Minkowski理论起源于Lutwak、Yang和Zhang在2010年的研究。本文首先引入了内部包含原点的凸体的Orlicz附加，然后将L p Brunn-Minkowski不等式推广到Orlicz Brunn-Minkowski不等式。进一步，我们利用Orlicz Brunn-Minkowski不等式将L p Minkowski混合体积不等式推广到Orlicz混合体积不等式。
Abstract The Orlicz Brunn–Minkowski theory originated with the work of Lutwak, Yang, and Zhang in 2010. In this paper, we first introduce the Orlicz addition of convex bodies containing the origin in their interiors, and then extend the L p Brunn–Minkowski inequality to the Orlicz Brunn–Minkowski inequality. Furthermore, we extend the L p Minkowski mixed volume inequality to the Orlicz mixed volume inequality by using the Orlicz Brunn–Minkowski inequality.