On the topology and the boundary of N–dimensional RCD(K,N) spaces

Kapovitch, Vitali¹ ; Mondino, Andrea²

¹ Department of Mathematics, University of Toronto, Toronto, ON, Canada
² Mathematical Institute, University of Oxford, Oxford, United Kingdom

Geometry & topology, Tome 25 (2021) no. 1, pp. 445-495.

Résumé

We establish topological regularity and stability of $N$–dimensional $\mathsf{RCD}\left(K,N\right)$ spaces (up to a small singular set), also called noncollapsed $\mathsf{RCD}\left(K,N\right)$ 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.

Détail

DOI : 10.2140/gt.2021.25.445

Classification : 53C23, 53C21
Keywords: Ricci curvature, optimal transport, metric measure spaces

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