Complete Flat Cone Metrics on Punctured Surfaces
Metric Geometry
2019-04-10 v3
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.
Keywords
Cite
@article{arxiv.1602.04240,
title = {Complete Flat Cone Metrics on Punctured Surfaces},
author = {İsmail Sağlam},
journal= {arXiv preprint arXiv:1602.04240},
year = {2019}
}
Comments
25 pages and 11 figures