Orlicz affine isoperimetric inequalities for star bodies

Youjiang Lin Chongqing Technology and Business University Dongmeng Xi Shanghai University

Convex and Discrete Geometry mathscidoc:2112.40004

Advances in Applied Mathematics, 2021.12
The original goal of this paper is to extend the affine isoperimetric inequality and Steiner type inequality of Orlicz projection bodies (which originated to Lutwak, Yang, and Zhang [36]), from convex bodies to Lipschitz star bodies (whose radial functions are locally Lipschitz). In order to achieve it, we investigate the graph functions of the given Lipschitz star body K: Along almost all directions u, we can define the graph functions on an open dense subset of the orthogonal projection of K onto u⊥.
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  title={Orlicz affine isoperimetric inequalities for star bodies},
  author={Youjiang Lin, and Dongmeng Xi},
  booktitle={Advances in Applied Mathematics},
Youjiang Lin, and Dongmeng Xi. Orlicz affine isoperimetric inequalities for star bodies. 2021. In Advances in Applied Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20211226211548257571891.
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