高斯迷向凸体  

Gaussian Isotropic Convex Bodies

作　　者：王雷[1] 何斌吾[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海大学学报（自然科学版）》2011年第3期266-269,共4页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11071156)

摘　　要：给出高斯迷向凸体和高斯迷向常数的定义,证明高斯迷向凸体的存在性和正交不变性等.另外,通过对单位体积球体和方体的高斯迷向常数进行计算,发现其具有与Lebesgue测度下凸体迷向常数变化相反的性质.Gaussian isotropic bodies and Gaussian isotropic constants were defined,and the existence and orthogonal invariability of Gaussian isotropic bodies were proved.By calculating the Gaussian isotropic constants of a ball and a cube,both with unit volume,we show that changes in the Gaussian isotropic constants in the Gaussian measure are opposite to those in the Lebesgue measure.

关 键 词：凸体 高斯测度 迷向常数 

分 类 号：O186.5[理学—数学]