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.
出处
《数学杂志》
CSCD
北大核心
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)
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
projection body
cone volume functional
centro-affine invariant
convex poly- tope
Parallelogram
