Orlicz mixed projection body

Abstract

In the paper, our main aim is to generalize the mixed projection body Π(K 1 ,...,K n−1 ) of (n − 1) convex bodies K 1 ,...,K n−1 to the Orlicz space. Under the framework of Orlicz-Brunn-Minkowski theory, we introduce a new geometric operation call it Orlicz mixed projection body Π φ (K 1 ,...,K n ) of n convex bodies K 1 ,...,K n . The new affine geometric quantity in special case yields the classical mixed projection body Π(K 1 ,...,K n−1 ) and Orlicz projection body Π φ K of K, respectively. As applications, Alesandrov-Fenchel type inequalities for the Orlicz mixed projection body are also established.