General Higher Order L^p Mean Zonoids

2023/12/15 by Dylan Langharst, Langharst, Dylan, Dongmeng Xi +1 · 1 citation
Mathematics · #Point processes and geometric inequalities #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2312.09500

Abstract

In 1970, Schneider introduced the higher-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the concept to a burgeoning higher-order Brunn-Minkowski theory. In 1991, Zhang introduced mean zonoids of a convex body, which was extended to the Firey-Brunn-Minkowski theory setting by Xi, Guo and Leng in 2014. In this note, we extend these L^p mean zonoids to the higher-order setting and establish the associated isoperimetric inequality.

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