Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms

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

• radial blaschke-minkowski homomorphism
• star duality
• brunn-minkowski inequality
• monotonic inequality
• shephard-type problem
• dual quermassintegral
• 52a20
• 52a39
• 52a40