Orlicz-Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms

Abstract

In this paper, we extend the Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms to an Orlicz setting and an Orlicz-Brunn- Minkowski inequality for radial Blaschke-Minkowski homomorphisms is established. The new Orlicz-Brun-Minkowski inequality in special case yields the Lp-Brunn- Minkowski inequality for the radial mixed Blaschke-Minkowski homomorphisms and the mixed intersection bodies, respectively.

Mathematics Subject Classication (2010): 52A20, 52A40.

Key words: Orlicz radial addition, intersection body, radial Blaschke-Minkowski homo-
morphisms, Orlicz dual mixed volume, Orlicz dual Brunn-Minkowski inequality.