Classification of Punctures on Complete Flat Surfaces

Yıl 2021, Cilt: 14 Sayı: 2, 266 - 276, 29.10.2021

İsmail Sağlam

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

Öz

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.

Anahtar Kelimeler

Flat surface, regular puncture, irregular puncture, conical singularities

Proje Numarası

18119001

Kaynakça

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