General Higher Order $L^p$ Mean Zonoids
Metric Geometry
2025-06-04 v3 Functional Analysis
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 mean zonoids to the higher-order setting and establish the associated isoperimetric inequality.
Cite
@article{arxiv.2312.09500,
title = {General Higher Order $L^p$ Mean Zonoids},
author = {Dylan Langharst and Dongmeng Xi},
journal= {arXiv preprint arXiv:2312.09500},
year = {2025}
}
Comments
12 pages, Keywords: Projection bodies, Centroid bodies, $L^p$ Busemann-Petty centroid inequality, radial mean bodies, mean zonoids. v2-3: Typo fixes, presentation of radial mean bodies updated