<i>L_p</i> Radial Blaschke-Minkowski Homomorphisms and <i>L_p</i> Dual Affine Surface Areas

Abstract

Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster’s results. In this paper, associated with L p dual affine surface areas, we give an affirmative and a negative form of the Busemann-Petty problem and establish two Brunn-Minkowski inequalities for the L p radial Blaschke-Minkowski homomorphisms.

Keywords

• Busemann-Petty problem
• <i>L_p</i> radial Blaschke-Minkowski homomorphism
• <i>L_p</i> dual affine surface area
• Brunn-Minkowski inequality