The geometry of Euclidean surfaces with conical singularities

2013/06/07 by Charalampos Charitos, Charitos, Charalampos, Ioannis Papadoperakis +3
Mathematics · #53C22 #57M50 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1306.1759

openalex publication_date 2013/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points. Dynamical properties for the space of geodesics are also proved.

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