数学季刊 ›› 2024, Vol. 39 ›› Issue (2): 180-184.doi: 10.13371/j.cnki.chin.q.j.m.2024.02.006
方晗兵1, 许斌2, 杨百瑞3
FANG Han-bing1, XU Bin2, YANG Bai-rui3
摘要: 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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