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On the topology and the boundary of $N$–dimensional $\mathsf{RCD}(K,N)$ spaces

Vitali Kapovitch and Andrea Mondino

Geometry & Topology 25 (2021) 445–495

We establish topological regularity and stability of N–dimensional RCD(K,N) spaces (up to a small singular set), also called noncollapsed RCD(K,N) 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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Ricci curvature, optimal transport, metric measure spaces
Mathematical Subject Classification 2010
Primary: 53C23
Secondary: 53C21
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
Vitali Kapovitch
Department of Mathematics
University of Toronto
Toronto, ON
Andrea Mondino
Mathematical Institute
University of Oxford
United Kingdom