Tohoku Mathematical Journal
2011
March
SECOND SERIES VOL. 63, NO. 1

Tohoku Math. J.
63 (2011), 59-76

Title A TOPOLOGICAL SPLITTING THEOREM FOR WEIGHTED ALEXANDROV SPACES

Author Kazuhiro Kuwae and Takashi Shioya

(Received March 31, 2009, revised April 4, 2010)
Abstract. Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting theorem for Riemannian manifolds with singularities of nonnegative (Bakry-Emery) Ricci curvature.

2000 Mathematics Subject Classification. Primary 53C20; Secondary 53C21, 53C23.
Key words and phrases. Splitting theorem, Ricci curvature, Bishop-Gromov inequality.

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