凸体的锥体积测度的一些注记  

Some remarks for cone-volume measure of convex bodies

作　　者：汤官华 TANG Guanhua(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第3期509-518,共10页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11371239)

摘　　要：锥体积测度在凸几何分析中扮演着重要的角色.给出了"正交补变换"的定义,并且证明了关于凸体的锥体积测度的两个命题等价.最后,给出了相关的性质及应用.The cone-volume measure plays an important role in convex geometric analysis.The definition of the complementary and orthogonal transformation is given in the paper.The equivalent of two propositions which is about the conevolume measure of convex bodies is proved.Finally,the properties and applications which are related to the cone-volume measure of convex bodies are given.

关 键 词：锥体积测度 凸体 RADON测度 高斯映射 支撑函数 

分 类 号：O186.5[理学—数学]