Reverse Minkowski Inequality For The Dual Quermassintegrals Of Mixed Intersection Bodies

The classical Brunn-Minkowski theory can date back to the dissertation of H.Brunn and the creation of H.Minkowski.Driven by mathematicians such as Bonnesen,Santalo,Fenchel,Blaschke and Busemann,the theory of convex geometry has well been prosperous and developed to be a significant branch of geometry.In 1975,Lutwak introduced the definition of a star bodies for the first time in”Dual Mixed Volumes”,and established the dual Brunn-Minkowski theory,which is the key for solving Busemann-Petty problem.Since the 1980s,the theory of convex bodies and star bodies has made great achievements,such as Lp-Brunn-Minkowski and Oricz-Brunn-Minkowski theory.The first two chapters of this thesis introduce the research background and preliminaries,respectively.The third chapter and the fourth one are the main con-tents of this article.some inequalities are established in the dual Brunn-Minkowski theory for intersection bodies.In the third chapter,the inverse Minkowski inequal-ity for dual quermassintergral of the mixed intersection bodies is proved by using Poya-Szego inequality and Holder inequality.Based on this,I shall extended the coefficients 0 ?i?n and 0 ? j ? n-1 for 0?i,0?j.In last chapter,I shows the inverse Brunn-minkowski inequality for dual quermassintegral of mixed intersection bodies by using inverse Minkowski inequality.