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On
the topology and the boundary of $N$–dimensional
$\mathsf{RCD}(K,N)$ spaces
Vitali Kapovitch and Andrea Mondino |
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Geometry & Topology 25 (2021) 445–495
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Abstract |
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We establish topological regularity and stability of –dimensional spaces (up to a small singular set), also called noncollapsed in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov–Hausdorff convergence. |
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Keywords
Ricci curvature, optimal transport, metric measure spaces
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Mathematical Subject Classification 2010
Primary: 53C23
Secondary: 53C21
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References |
Publication
Received: 15 August 2019
Revised: 29 February 2020
Accepted: 31 March 2020
Published: 2 March 2021
Proposed: Tobias H Colding
Seconded: David M Fisher, Bruce Kleiner
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Authors |
| Vitali Kapovitch | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| Andrea Mondino | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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