Complete flat cone metrics on punctured surfaces

Authors: İSMAİL SAĞLAM

Abstract: We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.

Keywords: Flat metric, the Gauss-Bonnet formula, surfaces with punctures, the Hopf-Rinow theorem

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