A topological splitting theorem for weighted Alexandrov spaces

Details A topological splitting theorem for weighted Alexandrov spaces A topological splitting theorem for weighted Alexandrov spaces

2009-03-30

arxiv.org/abs/0903.5150v2

Mathematics

Differential Geometry

20 pages to appear in Tohoku Mathematical Journal

Scientific paper

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.

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