锥体积泛函与仿射不等式(英文)  

CONE VOLUME FUNCTIONALS AND AFFINE INEQUALITIES

作　　者：熊革[1] 徐建荣[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《数学杂志》2011年第6期1049-1056,共8页Journal of Mathematics

基　　金：supported by NSFC(11001163);Innovation Program of Shanghai Municipal Education Commission(11YZ11);Shanghai Leading Academic Discipline Project(J50101)

摘　　要：本文研究了凸多胞形的锥体积泛函.利用投影体以及Lutwak、杨和张最近所建立的仿射等周不等式,得到了刻划平行四边形特征的一个崭新不等式和用锥体积泛函以及投影体的体积所表达的关于配极体体积的严格下界.In this paper, we mainly study the cone volume functionals for convex polytopes. By using projection bodies and the recently established affine isoperimetric inequality by Lutwark, Yang and Zhang, we obtain a new inequality characterizing parallelograms and the sharp lower bound for the volumes of polar bodies in terms of the cone volume functionals and volumes of projection bodies.

关 键 词：投影体 锥体积泛函 中心仿射不变 凸多胞形 平行四边形 

分 类 号：O186.5[理学—数学]