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.
Citation
Kazuhiro Kuwae. Takashi Shioya. "A topological splitting theorem for weighted Alexandrov spaces." Tohoku Math. J. (2) 63 (1) 59 - 76, 2011. https://doi.org/10.2748/tmj/1303219936
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