The Inequality Problem Of Orlicz Mixed Dual Harmonic Homogeneous Integral

The classical Brunn-Minkowski theory constitutes the core of modern convex geometry.During the last few decades,the classical Brunn-Minkowski theory developed quickly intoL_p Brunn-Minkowski theory.Recently,the Orlicz Brunn-Minkowski theory has been extended by Lutwak,Yang,Zhang and Gardner,Hug,Weil and other authors.The dual Orlicz Brunn-Minkowski theory was established by Gardner,Hug,Weil and Ye and other authors.This dissertation belongs to Dual Orlicz Brunn-Minkowski theory.It mainly uses the basic knowledge and concepts of Orlicz Brunn-Minkowski theory to study the Orlicz Brunn-Minkowskitypeinequalitiesformixeddualharmonichomogeneous integrals.Based on the definition of mixed dual harmonic homogeneous integral,the Orlicz first-order variations of dual harmonic homogeneous integral are calculated from the Orlicz addition operation of convex body,and the mixed dual harmonic homogeneous integral of convex body is derived.Furthermore,the support functions of two convex Orlicz combinations are defined by the Orlicz addition method of convex bodies,and the inclusion relations of convex bodies and subspace truncation are analyzed by the definition of support functions.We prove their Minkowski-type isoperimetric inequalities.Finally,we establish Orlicz Brunn-Minkowski-type inequalities for dual harmonic homogeneous integrals.