Dual Orlicz-Brunn-Minkowski theory: Orlicz φ-radial addition, Orlicz L_ϕ-dual mixed volume and related inequalities

2014/04/28 by Deping Ye, Ye, Deping · 1 citation
Mathematics · Physics and Astronomy · #52A20 #53A15 #Astronomical and nuclear sciences #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.DG #math.FA #math.MG #msc:52A20 #msc:53A15

paper · pdf · doi:10.48550/arxiv.1404.6991

arxiv created 2014/04/28 · openalex publication_date 2014/04/28 · arxiv updated 2014/04/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz φ-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz φ-radial addition of two star bodies, we derive a formula for the Orlicz L_ϕ-dual mixed volume. Moreover, a dual Orlicz-Minkowski inequality for the Orlicz L_ϕ-dual mixed volume, a dual Orlicz isoperimetric inequality for the Orlicz L_ϕ-dual surface area and a dual Orlicz-Urysohn inequality for the Orlicz L_ϕ-harmonic mean radius are proved.

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• The Dual Orlicz-Brunn-Minkowski Theory

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