Schneider Projection Problem Related Cone Volume Inequality

The topic of this dissertation belongs to Convex Geometric Analysis.To study thewell-known Schneider’s projection problem，E．Lutwak，D．Yang and G．Zhang introduced anew affine invariant functional in n.Thereby,a real breakthrough for Schneider’s projectionproblem has gained.This dissertation studies a projection-related cone volume inequality.Firstly,this dissertation sketches the growing history and researching status of convexgeometry.The following,it emphatically studies the problem of the well-known Schneider’sprojection problem regarding to projection bodies. We obtain a new cone volume inequalityrestricted to the origin-symmetric convex bodies in n.Its application to Schneider’s projectionproblem will lead to a new conclusion for projection problem.