| 椭球的Orlicz质心体(英文) |
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| 引用本文： | 熊革,徐治华.椭球的Orlicz质心体(英文)[J].应用数学与计算数学学报,2012,26(1):94-101. |
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| 作者姓名： | 熊革 徐治华 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 凸体 支持函数 质心体 Orlicz质心体 |
Orlicz centroid bodies of ellipsoids |
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| XIONG Ge,XU Zhi-hua.Orlicz centroid bodies of ellipsoids[J].Communication on Applied Mathematics and Computation,2012,26(1):94-101. |
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| Authors: | XIONG Ge XU Zhi-hua |
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| Institution: | (College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | 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 functions of the Orlicz centroid bodies of the unit ball for specific convex functions are computed. |
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| Keywords: | convex body support function centroid body Orlicz centroid body |
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