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arXiv · 1912.01187

The Gauss-Bonnet formula of a conical metric on a compact Riemann surface

Hanbing Fang·Bin Xu·Bairui Yang
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Abstract

We prove a generalization of the classical Gauss-Bonnet formula for a conical metric on a compact Riemann surface provided that the Gaussian curvature is Lebesgue integrable with respect to the area form of the metric. We also construct explicitly some conical metrics whose curvature is not integrable.

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Hanbing Fang, Bin Xu, Bairui Yang. 2019-12-03. The Gauss-Bonnet formula of a conical metric on a compact Riemann surface. https://arxiv.org/abs/1912.01187

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