凸体的p-宽度积分

p-WIDTH-INTEGRALS OF CONVEX BODIES

本文研究了凸体p-宽度积分的问题,利用积分的方法,建立了有关凸体p-宽度积分的Brunn-Minkowski型不等式,Blaschke-Santal型不等式.作为应用,获得了Lp-投影体极,Lp-质心体极的Brunn-Minkowski型不等式.

In this paper, we introduce the conception of the p-width-integrals of convex bodies and get some properties. By applying the integral methods, we establish some inequalities of the p-width-integrals of convex bodies. As an application, the Brunn-Minkowski type inequality for polar duality of Lp-projection bodies and Lp-centroid bodies is abtained.