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

Kapovitch, Vitali; Mondino, Andrea

doi:10.2140/gt.2021.25.445

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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

DOI: 10.2140/gt.2021.25.445

Abstract

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.

Keywords

Ricci curvature, optimal transport, metric measure spaces

Mathematical Subject Classification 2010

Primary: 53C23

Secondary: 53C21

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

Authors

Vitali Kapovitch
Department of Mathematics University of Toronto Toronto, ON Canada

Andrea Mondino
Mathematical Institute University of Oxford Oxford United Kingdom

Volume 25, issue 1 (2021)