The Orlicz Brunn-minkowski Inequality For Dual Harmonic Quermassintegrals

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 it was extended to the Orlicz Brunn-Minkowski theory.This dissertation belongs to the dual Orlicz Brunn-Minkowski theory,and devotes to the study of the Orlicz Brunn-Minkowski type inequality for dual harmonic quermassintegrals.In this dissertation,based on the definition of dual harmonic quermassintegrals,starting from the Orlicz radial addition of star bodies,the first Orlicz variations of dual harmonic quermassintegrals are calculated.We furtherly introduce the notion of Orlicz dual mixed harmonic quermassintegrals for star body.For the class of new geometric quantities,we prove their Minkowski type isoperimetric inequality.And on this basis,the Orlicz Brunn-Minkowski type inequality for dual harmonic quermassintegrals is established.