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On the topology and the boundary of N-dimensional RCD(K,N) spaces
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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.
Forward citations
Cited by 3 Pith papers
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On the structure of RCD spaces with upper curvature bounds
Every RCD space with curvature bounded above is a topological manifold with boundary whose interior is the regular set, a smooth geodesically convex manifold.
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Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces
In RCD(K,N) spaces, the reduced boundary of a set of finite perimeter has a unique Euclidean half-space tangent at almost every point and is rectifiable by bi-Lipschitz charts.
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Lipschitz continuity of harmonic maps between ${\rm RCD}(K,N)$ spaces and ${\rm CAT}(\kappa)$ spaces
Energy-minimizing harmonic maps from RCD(K,N) domains into small balls in CAT(κ) spaces are locally Lipschitz, completing the singular Bochner–Eells–Sampson picture.
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