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

By V. Kapovitch, Andrea Mondino. Geometry and Topology, 2019

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We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0239d808a892cfd7c57d3756d1ef8aff725e4462