The Isoperimetric Inequality Of The General Orlicz Mixed Centroid Body

Centroid body is a basic concept in convex geometric analysis,which has im-portant applications in information theory,analysis and other fields.Especially,centroid inequalities of centroid bodies are widely used in those fields.In this thesis,for a class of convex function ?? and m variables,we define the general Orlicz mixed centroid body.Then,we establish the isoperimetric inequality of the general Orlicz mixed centroid body.In particular,when m = 1,? = 0 and the density function is the characteristic function of a convex body whose volume is 1,we obtain the concept of the general Orlicz mean zonoid about probability measure and the cor-responding affine isoperimetric inequality.Furthermore,as a corollary,we extend the Lp centroid body about probability measure to more general cases,and get the concept of the Lp centroid body about probability measure and the corresponding affine isoperimetric inequality.