English

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

R2 v1 2026-06-22T12:49:25.255Z