Complete Flat Cone Metrics on Punctured Surfaces
  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. 
\.Ismail Sa\u{g}lam
math.MG