2025/04/04 by Charalampos Charitos, Charitos, Charalampos, Ioannis Papadoperakis +3
Mathematics · #53C20 #53C23 #53C45 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2504.03356
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≤ 0 is given.