English

Classification of punctures on complete flat surfaces

Metric Geometry 2020-02-13 v1

Abstract

We investigate the behavior of a complete flat metric on a surface near a puncture. We call a puncture on a flat surface regular if it has a neighborhood which is isometric to that of a point at infinity of a cone. We prove that there are punctures which are not regular if and only if the curvature at the puncture is 4π4\pi.

Keywords

Cite

@article{arxiv.2002.04994,
  title  = {Classification of punctures on complete flat surfaces},
  author = {İsmail Sağlam},
  journal= {arXiv preprint arXiv:2002.04994},
  year   = {2020}
}
R2 v1 2026-06-23T13:39:36.196Z