The New Inequalities Of The Star Body And A Note Of The Minkowski Inequality

In the first part of this paper, we investigate convex geometric inequalities on the star body. Firstly some new inequalities of star body are given. After we give the definition of a new chord integral of the star body,the inequalities of chord symmetry and intersection body of star body can be obtained. And then we extend inequalities for the width integral and star bodies by virtue of a correct proof of a known quermassintegral inequaliy.In the second part, we give a simplified proof of the Minkowski inequality for the mixed area of tuo plane convex sets.