Curvature bounds of subsets in dimension two

2021/05/03 by Alexander Lytchak, Lytchak, Alexander, Stephan Stadler +1
Computer Science · Mathematics · #53C22 #53C23 #54F65 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2105.00726

openalex publication_date 2021/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that closed subsets with vanishing first homology in two-dimensional spaces inherit the upper curvature bound from their ambient spaces and discuss topological applications.

Citations

• Vietoris-Rips Persistent Homology

Related

• Topological regularity of spaces with an upper curvature bound
• Improvements of upper curvature bounds
• Geodesically complete spaces with an upper curvature bound
• Two-dimensional metric spaces with curvature bounded above II
• Topological representation of the geometry of metric spaces