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

Vitali Kapovitch; Andrea Mondino

doi:10.2140/gt.2021.25.445

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arXiv · 1907.02614

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

Vitali Kapovitch·Andrea Mondino

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Abstract

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.

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Vitali Kapovitch, Andrea Mondino. 2020-03-31. On the topology and the boundary of N-dimensional RCD(K,N) spaces. https://doi.org/10.2140/gt.2021.25.445

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