Dual Quermassintegrals Inequalities Of Some Star Bodies

This paper based on the dual Brunn-Minkowski theory, stars as the research object, used convex body geometry theory and functional analysis method, combined with Clarkson inequality,Bellman inequality,Minkowski integral inequality,Holder integral inequality such as analytic inequality, established a series of dual quermassintegrals inequalities.The dual quermassintegrals is a special form of mixed volume, corresponding to quermassintegrals of the classical theory. The development survey and main re-search directions of convex geometry are presented in the preface, and the main result were given. In Chapter 2, we set up the dual quermassintegrals inequalities of the quotient star bodies. In addition, a few simple and symmetric dual quermass-integrals inequalities in n-dimensional Euclidean space were completed. In Chapter 3, we presented the extensions of dual Minkowski inequality of the dual quermass-integrals. In Chapter 4, established the dual Minkowski inequality and the dual Brunn-Minkowski inequality of the dual quermassintegrals, which is relate to the mixed intersection body, and the dual Brunn-Minkowski inequality of the mixed p-dual affine quermassintegrals about reconciling Blaschke linear combination of were given.