2023/12/04 by Tianqi Wu, Wu, Tianqi
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2312.01704
openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a triangulated surface, a polyhedral metric could be constructed by gluing Euclidean triangles edge-to-edge. We carefully describe the construction and prove that such a polyhedral metric is the only intrinsic metric on the glued surface that preserves the lengths of the curves on the Euclidean triangles. We also discuss the edge length coordinates of the Teichmüller space of the polyhedral metrics on a marked surface.