Cyclic Brunn-Minkowski Inequalities for the General L p -Mixed Brightness Integrals and General L p -Dual

Mixed Brightness Integrals

Linmei Yu, Weidong Wang ∗ and Yuanyuan Zhang

Abstract—Based on the general L p -projection bodies, Yan and Wang introduced the notion of general L p -mixed brightness integrals. Combining with general L p -intersection bodies, Zhang and Wang gave the general L p -dual mixed brightness integrals. In this paper, we establish the new cyclic Brunn-Minkowski inequalities for general L p -mixed brightness integrals and general L p dual mixed brightness integrals. Our results unify the relevant cyclic inequalities and Brunn-Minkowski inequalities.

Index Terms—cyclic inequality; Brunn-Minkowski inequality; L p -mixed brightness integral; L p -dual mixed brightness integral.