The Orlicz Brunn-Minkowski inequality

Dongmeng Xi Shanghai University Hailin Jin Shanghai University Gangsong Leng Shanghai University

Convex and Discrete Geometry mathscidoc:1703.40035

Advances in Mathematics, 260, 350-374, 2014.5
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 Lp Brunn-Minkowski inequality to the Orlicz Brunn-Minkowski inequality. Furthermore, we extend the Lp Minkowski mixed volume inequality to the Orlicz mixed volume inequality by using the Orlicz Brunn-Minkowski inequality.
Convex body, Orlicz addition, Orlicz Brunn-Minkowski inequality, Orlicz mixed volume.
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  title={The Orlicz Brunn-Minkowski inequality },
  author={Dongmeng Xi, Hailin Jin, and Gangsong Leng},
  booktitle={Advances in Mathematics},
Dongmeng Xi, Hailin Jin, and Gangsong Leng. The Orlicz Brunn-Minkowski inequality . 2014. Vol. 260. In Advances in Mathematics. pp.350-374.
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