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Tohoku Mathematical Journal
SECOND SERIES VOL. 63, NO. 1
|Tohoku Math. J.|
63 (2011), 59-76
A TOPOLOGICAL SPLITTING THEOREM FOR WEIGHTED ALEXANDROV SPACES
Kazuhiro Kuwae and Takashi Shioya
(Received March 31, 2009, revised April 4, 2010)
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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