Some inequalities for star duality of the radial

Blaschke-Minkowski homomorphisms

Xia Zhao, Weidong Wang*, and Youjiang Lin

Abstract: In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

Keywords:radialBlaschkeMinkowskihomomorphism,starduality,Brunn-Minkowskiinequality,monotonicinequality, Shephard-type problem, dual quermassintegral