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锥体积泛函与仿射不等式(英文)
引用本文:熊革,徐建荣.锥体积泛函与仿射不等式(英文)[J].数学杂志,2011,31(6):1049-1056.
作者姓名:熊革  徐建荣
作者单位:上海大学数学系,上海,200444
基金项目:Research of the first author is NSFC,Innovation Program of Shanghai Municipal Education Commission,Shanghai Leading Academic Discipline Project
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.

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

CONE VOLUME FUNCTIONALS AND AFFINE INEQUALITIES
XIONG Ge,XU Jian-rong.CONE VOLUME FUNCTIONALS AND AFFINE INEQUALITIES[J].Journal of Mathematics,2011,31(6):1049-1056.
Authors:XIONG Ge  XU Jian-rong
Institution:XIONG Ge,XU Jian-rong (Department of Mathematics,Shanghai University,Shanghai 200444,China)
Abstract: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.
Keywords:projection body  cone volume functional  centro-affine invariant  convex polytope  Parallelogram
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