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 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.展开更多
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).
文摘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.
