Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces

2020/07/16 by Marcel Vinhas, Vinhas, Marcel
Mathematics · #51F99 (Primary) #53C23 (Secondary) #53C45 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2007.08420

openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given metric quotients S and S_n, n ∈ ℕ, of a metric space X, sufficient conditions are provided on the data defining them guaranteeing that S is the Gromov-Hausdorff limit of S_n. These conditions are recognized within metric quotients of plane polygons determined by side-pairings known as plain paper-folding schemes. In particular, concrete examples are given of sequences of two-dimensional conic-flat spheres converging to spheres that are conic-flat except around certain singularities, some of them with unbounded curvature in the sense of comparative geometry.

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