Total curvature of planar graphs with nonnegative combinatorial curvature

2017/03/12 by Bobo Hua, Hua, Bobo, Yanhui Su +1
Computer Science · Mathematics · #05C10 #31C05 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1703.04119

openalex publication_date 2017/03/12 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We prove that the total curvature of any planar graph with nonnegative combinatorial curvature is an integral multiple of (1)/(12). As a corollary, this answers a question proposed by T. Réti.

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