General Higher Order $L^p$ Mean Zonoids

Fuente: arXiv
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Main Authors: Langharst, Dylan, Xi, Dongmeng
Format: Preprint
Published: 2023
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author Langharst, Dylan
Xi, Dongmeng
author_facet Langharst, Dylan
Xi, Dongmeng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_09500
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle General Higher Order $L^p$ Mean Zonoids
Langharst, Dylan
Xi, Dongmeng
Metric Geometry
Functional Analysis
52A30, 52A40, Secondary: 28A75
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.
title General Higher Order $L^p$ Mean Zonoids
topic Metric Geometry
Functional Analysis
52A30, 52A40, Secondary: 28A75
url https://arxiv.org/abs/2312.09500