A topological splitting theorem for weighted Alexandrov spaces
Differential Geometry
2010-10-01 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.0903.5150,
title = {A topological splitting theorem for weighted Alexandrov spaces},
author = {Kazuhiro Kuwae and Takashi Shioya},
journal= {arXiv preprint arXiv:0903.5150},
year = {2010}
}
Comments
20 pages to appear in Tohoku Mathematical Journal