Journal of East China Normal University(Natural Sc ›› 2007, Vol. 2007 ›› Issue (5): 1-11.

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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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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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