Geodesically complete spaces with an upper curvature bound

By A. Lytchak, Koichi Nagano. Geometric and Functional Analysis, 2018

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We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity of the metric structure on a large part.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eb49ce3108c5c607f5a019b436f8b86a267b9012