Shephard type problem for <i>L_p</i>-mixed Blaschke-Minkowski homomorphisms

Abstract

In 2006, Schuster introduced the concept of Blaschke-Minkowski homomorphism of convex bodies. In this paper, we introduce the L_p-mixed Blaschke-Minkowski homomorphism in L_p-Brunn-Minkowski theory. We then further study the Shephard type problem involving an affirmative answer and two negative answers for L_p-mixed Blaschke-Minkowski homomorphism.