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许斌教授学术报告

  发布日期:2018-1-2  浏览量:755


报告题目一Conformal hyperbolic metrics and bounded projective functions with singularities

报 告 人:许斌(中国科学技术大学,副教授)

报告时间:2018年1月11号(周四)上午9:30-11:00

报告地点磬苑校区数学科学学院H113

报告摘要More than half an century ago, J. Nitsche showed that isolated singularities of conformal hyperbolic metrics are either cusp singularities or cone ones, and M. Heins proved that the Gauss-Bonnet formula actually forms a necessary and sufficient condition for the existence of conformal hyperbolic metrics with isolated singularities on compact Riemann surfaces. Projective functions are multi-valued locally univalent meromorphic functions on Riemann surfaces such that their monodromy lies in the group PGL(2,C) consisting of all Möbius transformations.

From the viewpoint of Complex Analysis, by using the analysis of PDE, we characterized conformal hyperbolic metrics with finitely many singularities on compact Riemann surfaces by bounded projective functions on the punctured surface by the singularities such that the  Schwarzian derivative of the projective functions have double poles with coefficients prescribed by the angles of the singularities.

This is a joint work with Bo Li and Long Li.

 

 

报告题目二Cone spherical metrics on compact Riemann surfaces

报 告 人:许斌(中国科学技术大学,副教授)

报告时间:2018年1月12号(周五)上午9:30-11:00

报告地点磬苑校区数学科学学院H113

报告摘要Cone spherical, flat and hyperbolic metrics are conformal metrics with constant curvature +1; 0 and -1, espectively, and with finitely many conical singularities on compact Riemann surfaces. The Gauss-Bonnet formula gives a natural necessary condition for the existence of such three kinds of metrics with prescribed conical singularities on compact Riemann surfaces. The condition is also sufficient for both flat and hyperbolic metrics. However, it is not the case for cone spherical metrics, whose existence has been an open problem over thirty years. Projective functions are multi-valued locally univalent meromorphic functions on Riemann surfaces such that their monodromy lies in the roup PGL(2,C) consisting of all Möbius transformations. We observed that the developing maps of cone spherical metrics are projective functions on the surfaces punctured by the conical ngularities whose monodromy lie in PSU(2), and whose Schwarzian derivatives have double poles at the conical singularities with coefficients prescribed by the cone angles. Starting from this observation, we made some progresses on cone spherical metrics by using Complex Algebraic Geometry, which consist of the joint works with Qing Chen, Yiran Cheng, Bo Li, Lingguang Li, Santai Qu, Jijian Song and Yingyi Wu.

 

 

专家介绍

中国科学技术大学数学科学学院副教授。主要研究方向是微分几何。毕业于中国科技大学数学系,1997年留校任教。东京大学数理科学研究科博士,东京工业大学数学系博士后。已有的科研工作涉及偏微分方程,流形上的李变换群和流形上的分析,主要论文发表于.Ann.Global Anal.Geom.,Chin.Ann.Math.,Yokohama Publ.,Internat.J.Math.,J.Math.Soc.Japan等期刊。目前主要研究兴趣为紧致 Kahler 流形上的 Kahler-Einstein 度量与极值度量的几何,流形上的变换群理论,Euclidean 空间与紧致 Riemann 流形上的调和分析。


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