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arXiv · 2504.03356

Gluing $CAT(0)$ domains

Charalampos Charitos·Ioannis Papadoperakis·Georgios Tsapogas
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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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Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas. 2025-04-04. Gluing $CAT(0)$ domains. https://arxiv.org/abs/2504.03356

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