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Gluing $CAT(0)$ domains (2504.03356v1)
Published 4 Apr 2025 in math.DG, math.GT, and math.MG
Abstract: In this work we describe a class of subsets of the Euclidean plane which, with the induced length metric, are locally $CAT(0)$ spaces and we show that the gluing of two such subsets along a piece of their boundary is again a locally $CAT(0)$ space provided that the sum of the signed curvatures at every gluing point is non-positive. A generalization to subsets of smooth Riemannian surfaces of curvature $k\leq 0$ is given.
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