Triangulating metric surfaces

2021/02/12 by Paul Creutz, Creutz, Paul, Matthew Romney +1 · 1 citation
Mathematics · #53A05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary: 53C45 #Secondary: 52A10

paper · pdf · doi:10.48550/arxiv.2102.06667

openalex publication_date 2021/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any length metric space homeomorphic to a surface may be decomposed into non-overlapping convex triangles of arbitrarily small diameter. This generalizes a previous result of Alexandrov--Zalgaller for surfaces of bounded curvature.

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