The Properties Of Inclusion Measures Which Is In Intersection Of Halfspace And Mixed Volumes

The theory of convex geometry bodies mainly researches about the geo-metric properties of convex bodies and stars.Based on the Brunn-Minkowski theory, this thesis tries to use the notions, basic properties and integral trans-form methods of Brunn-Minkowski theory to introduce the inclusion measures inequlities and extremum of convex bodies. And in this paper, you’ll find we discuss it from the following two aspects:On the one hand, we’ll study it from the aspect of properties of halfspace intersection C(K1,K2,λ). On the other hand, we’ll research it from the aspect of properties of the inequlities of the quermassintegrals and the mixed volumes’.So the content of this paper is arranged as follows:In Chapter1,we introduce the history and development of application about the convex geometry bodies. And in chapter l,we also show the conclu-sion of the paper.In Chapter2,by researching the relationship between K1and K2in the halfspace intersection C(K1, K2,λ),we can get properties of C(K1,K2,λ), Furtherly the properties of inequlities of K2in inclusion measures can be ob-tained from the Equivalent relationship between the halfspace intersection and inclusion measure.In Chapter3,we use the properties of the convex mixed volumes inequli-ties and quermassintegrals transform to research inclusion measure inequli-ties.In this chapter,two extremum inequlities are established.In Chapter4,according to the relationship between the cross section body and the centrosome in the convex body,we establish the related inclusion mea-sure equation, Then we consider the properties of the cross section body itself and its application on inclusion measure of oval to get the equation of oval inclusion measure.