Some inequalities for <i>L_p</i> radial Blaschke-Minkowski homomorphisms¹

Abstract

The notion of radial Blaschke-Minkowski homomorphisms was presented by Schuster. Afterwards, Wang et al. introduced L_p radial Blaschke-Minkowski homomorphisms. In this paper, associated with L_p-dual affine surface areas, we establish some inequalities including the Brunn-Minkowski type inequality, cyclic inequality and monotonic inequalities, and give an affirmative answer and a negative answer of Busemann-Petty problem for the L_p radial Blaschke-Minkowski homomorphisms.

Mathematics Subject Classification (2010): 52A20, 52A40, 52A39.

Keywords: L_p radial Blaschke-Minkowski homomorphism, L_p-dual affine surface area, Brunn-Minkowski inequality, monotonic inequality, Busemann-Petty problem