Orlicz mixed radial Blaschke–Minkowski homomorphisms

Abstract

Our main aim is to generalize the mixed radial Blaschke–Minkowski homomorphisms to the Orlicz space. By calculating first-order variation of the harmonic p-dual quermassintegrals of mixed radial Blaschke–Minkowski homomorphisms, we introduce a new affine geometric quantity and call it Orlicz mixed radial Blaschke–Minkowski homomorphisms. The Orlicz–Minkowski inequality for Orlicz mixed radial Blaschke–Minkowski homomorphisms is established. As an application, an Orlicz–Brunn–Minkowski inequality for the mixed radial Blaschke–Minkowski homomorphisms is also established, which in special case yields new $$L_p$$ Brunn–Minkowski inequality for mixed radial Blaschke–Minkowski homomorphisms.