华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (5): 1-11.

• 数学 统计学 •    下一篇

关于加权熵公式的几点注记（英）

王林峰1,2   

  1. 1. 华东师范大学 数学系, 上海 200062; 2.南通大学 数学系, 江苏 南通 200062
  • 收稿日期:2006-09-28 修回日期:2007-01-17 出版日期:2007-09-25 发布日期:2007-09-25
  • 通讯作者: 王林峰

Some Remarks on the Weighted Entropy(English)

WANG Lin-feng1,2

  

  1. 1. epartment of Mathematics, East China NormalUniversity, Shanghai 200062, China ; 2. Department of Mathematics, Nantong University, Nantong Jiangsu 226000, ina
  • Received:2006-09-28 Revised:2007-01-17 Online:2007-09-25 Published:2007-09-25
  • Contact: WANG Lin-feng

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摘要： 给出加权熵沿加权热方程的单调性,
研究了加权热核短时间的性态, 指出加权熵可以视作某种等周常数,
并且利用它讨论流形的若干几何性质.

关键词: 热核, 权熵, akry-Emery曲率张量, 体积增长, 热核, 权熵, akry-Emery曲率张量, 体积增长

Abstract: This paper gave the monotonicity of weighted entropy,
studied the short time behavior of the weighted heat kernel, showed
the entropy can be regarded as an isoperimetric constant,
and used it to discuss some geometric properties of the manifold.

Key words: weighted entropy, Bakry-Emery curvature tensor, olume growth, heat kernel, weighted entropy, Bakry-Emery curvature tensor, olume growth

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