A topological splitting theorem for weighted Alexandrov spaces

Kazuhiro Kuwae; Takashi Shioya

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arXiv · 0903.5150

A topological splitting theorem for weighted Alexandrov spaces

Kazuhiro Kuwae·Takashi Shioya

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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.

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Kazuhiro Kuwae, Takashi Shioya. 2010-09-30. A topological splitting theorem for weighted Alexandrov spaces. https://arxiv.org/abs/0903.5150

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