Orlicz--Lorentz centroid bodies

2016/12/09 by Van Hoang Nguyen, Nguyen, Van Hoang
Mathematics · #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1612.03215

openalex publication_date 2016/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the definition of the centroid body operator to an Orlicz--Lorentz centroid body operator on the star bodies in \mathbb Rⁿ, and establish the sharp affine isoperimetric inequality that bounds (from below) the volume of the Orlicz--Lorentz centroid body of any convex body containing the origin in its interior by the volume of this convex body.

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