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arXiv · 1602.04240

Complete Flat Cone Metrics on Punctured Surfaces

İsmail Sağlam
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Abstract

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

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İsmail Sağlam. 2017-06-24. Complete Flat Cone Metrics on Punctured Surfaces. https://doi.org/10.3906/mat-1806-23

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