Classification of Punctures on Complete Flat Surfaces

Year 2021, Volume: 14 Issue: 2, 266 - 276, 29.10.2021

İsmail Sağlam

https://doi.org/10.36890/iejg.784598

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 $4\pi$. We classify irregular punctures of a flat surface up to modification equivalence, where two punctures are called modification-equivalent if they have isometric neighborhoods. We show that there are uncountably many modification-equivalence classes of punctures on flat surfaces.

Keywords

Flat surface, regular puncture, irregular puncture, conical singularities

Project Number

18119001

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