A topological splitting theorem for weighted Alexandrov spaces

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概要

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• 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.

著者

• Kuwae Kazuhiro

  Department Of Mathematics And Engineering Graduate School Of Science And Technology Kumamoto Univers

• Shioya Takashi

  Mathematical Institute, Tohoku University

• Shioya Takashi

  Mathematical Institute Tohoku University

関連論文

• A topological splitting theorem for weighted Alexandrov spaces
• Collapsing three-manifolds with a lower curvature bound
• On a Liouville type theorem for harmonic maps to convex spaces via Markov chains (Proceedings of RIMS Workshop on Stochastic Analysis and Applications)
• Convergence of Alexandrov spaces and spectrum of Laplacian
• On subharmonicity for symmetric Markov processes
• On subharmonicity for symmetric Markov processes

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