2020
DOI: 10.48550/arxiv.2002.04994
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Classification of punctures on complete flat surfaces

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 4π.

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