Orlicz--Lorentz centroid bodies

Abstract

We extend the definition of the centroid body operator to an Orlicz--Lorentz centroid body operator on the star bodies in ${\mathbb{R}}^n$, 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.

22 pages, to appear in Advances in Applied Mathematics