Mixed complex rightness integrals

Chao Li 1 · Weidong Wang 1,2 · Youjiang Lin 3

Abstract

The notion of the mixed brightness was first introduced by Lutwak. Recently, Abardia and Bernig presented complex projection bodies. Based on this notion, we define the mixed complex brightness integrals and establish related Aleksandrov–Fenchel inequality, cyclic inequality and monotonicity inequality, respectively.

Keywords Complex projection body · Mixed complex brightness integral ·Aleksandrov–Fenchel inequality ·Cyclic inequality · Monotonicity inequality