Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (6): 1949-1974.doi: 10.1016/S0252-9602(10)60185-3

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ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES

 ZHANG Hui-Chun, SHU Xi-Ping   

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2010-08-15 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The second author is partially supported by NSFC (10831008) and NKBRPC (2006CB805905).

Abstract:

Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we  extend our research to summarize the  geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume    comparison and Lipschitz continuity of heat kernel, are obtained.

Key words: Alexandrov spaces, Ricci curvature, volume comparison, heat kernel

CLC Number: 

  • 51F99
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