椭球的Orlicz质心体(英文)  

Orlicz centroid bodies of ellipsoids

作　　者：熊革[1] 徐治华[1] 

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》2012年第1期94-101,共8页Communication on Applied Mathematics and Computation

基　　金：Project supported by the National Natural Science Foundation of China(11001163);the Innovation Program of Shanghai Municipal Education Commission(11YZ11);the Shanghai Leading Academic Discipline Project(J50101)

摘　　要：主要研究了Lutwak等所引入的Orlicz质心体(Lutwak E,Yang D,Zhang G.Orliczcentroid bodies.J.Differential Geom.,2010,84:365-387).利用Orlicz质心体在线性变换下的不变性,证明了椭球的Orlicz质心体仍是椭球.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz质心体的支持函数.This paper studies the Orlicz centroid bodies introduced by Lutwak, et al. （Lutwak E, Yang D, Zhang G. Orlicz centroid bodies. J. Differential Geom., 2010, 84： 365-387）. By using the linear invariant property of the Orlicz centroid bodies, the fact that the Orlicz centroid bodies of ellipsoids are still ellipsoids is demonstrated. As examples, two concrete support flmctions of the Orlicz centroid bodies of the unit ball for specific convex functions are computed.

关 键 词：凸体 支持函数 质心体 Orlicz质心体 

分 类 号：O174[理学—数学]