Articles

ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES

  • ZHANG Hui-Chun ,
  • SHU Xi-Ping
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  • Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received date: 2010-08-15

  Online 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.

Cite this article

ZHANG Hui-Chun , SHU Xi-Ping . ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES[J]. Acta mathematica scientia, Series B, 2010 , 30(6) : 1949 -1974 . DOI: 10.1016/S0252-9602(10)60185-3

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