Gluing $CAT(0)$ domains
Differential Geometry
2025-04-07 v1 Geometric Topology
Metric Geometry
Abstract
In this work we describe a class of subsets of the Euclidean plane which, with the induced length metric, are locally spaces and we show that the gluing of two such subsets along a piece of their boundary is again a locally 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 is given.
Keywords
Cite
@article{arxiv.2504.03356,
title = {Gluing $CAT(0)$ domains},
author = {Charalampos Charitos and Ioannis Papadoperakis and Georgios Tsapogas},
journal= {arXiv preprint arXiv:2504.03356},
year = {2025}
}
Comments
32 pages, 9 figures