Communications in Analysis and Geometry

Volume 18 (2010)

Number 3

Ricci curvature on Alexandrov spaces and rigidity theorems

Pages: 503 – 553

DOI: http://dx.doi.org/10.4310/CAG.2010.v18.n3.a4

Authors

Hui-Chun Zhang (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Xi-Ping Zhu (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Abstract

In this paper, we introduce a new notion for lower bounds of Ricci curvature on Alexandrov spaces, and extend Cheeger–Gromoll splitting theorem and Cheng’s maximal diameter theorem to Alexandrov spaces under this Ricci curvature condition.

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