紧黎曼曲面上锥度量的高斯博内公式  

The Gauss-Bonnet Formula of a Conical Metric on a Compact Riemann Surface

作　　者：方晗兵 许斌 杨百瑞 FANG Han-bing;XU Bin;YANG Bai-rui(Mathematics Department,Stony Brook University,NY 11794,United States;CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]Mathematics Department,Stony Brook University,NY 11794,United States [2]CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China [3]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第2期180-184,共5页数学季刊（英文版）

基　　金：Support by the Project of Stable Support for Youth Team in Basic Research Field,CAS(Grant No.YSBR-001);NSFC(Grant Nos.12271495,11971450 and 12071449).

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.

关 键 词：Gauss-Bonnet formula Conical metric Riemann surface Gaussian curvature Lebesgue integrable 

分 类 号：O187.1[理学—数学]