Conformal metrics on Riemann surfaces with cusp singularities
Received date: 2016-01-29
Online published: 2016-11-15
Riemann面上带有奇点的度量是复几何中重要的研究对象.对Riemann面上带有cusp奇点且满足面积和Calabi能量有限的共形度量进行研究，得到HCMU度量在cusp奇点附近精确的表达式.
关键词： cusp奇点; extremal Hermitian度量; HCMU度量
国金宇 , 吴英毅 , 魏志强 . Riemann面上带cusp奇点的共形度量[J]. 中国科学院大学学报, 2016 , 33(6) : 721 -728 . DOI: 10.7523/j.issn.2095-6134.2016.06.001
The metric on Riemann surface with singularities is one of important objects in complex geometry. We study conformal metrics on Riemann surfaces with only cusp singularities,whose area and Calabi energy are both finite, and obtain the exact expression of HCMU metrics near cusp singularities.
Key words： cusp singularity; extremal Hermitian metric; HCMU metric
[1] Calabi E. Extremal Kähler metrics[C]//Seminar on Differential Geometry. Annals of Mathematical Studies 102, Princeton:Princeton Univ Press,1982:259-290.
[2] Chen X X. Weak limits of Riemannian metrics in surfaces with integral curvature bound[J]. Calc Var, 1998, 6:189-226.
[3] Chen Q, Chen X X, He W Y. Singular angles of weak limiting metrics under certain integral curvature bounds[J]. Pacific Journal of Mathematics, 2007,231(1):35-49.
[4] Chen X X. Extremal Hermitian metrics on Riemann surfaces[J]. Calc Var, 1999, 8:191-232.
[5] Wang G F, Zhu X H. Extremal Hermitian metrics on Riemann surfaces with singularities[J]. Duke Math Journal, 2000, 104(2):181-210.
[6] Chen Q, Wu Y Y. Character 1-form and the existence of an HCMU metric[J]. Mathematische Annalen, 2011, 351(2):327-345.
[7] Chen Q, Wu Y Y, Xu Bin. On one-dimensional and singular Calabi's extremal metrics whose Gauss curvatures have nonzero umbilical Hessians[J]. Isreal Journal of Mathematics, 2015, 208(1):385-412.
/
| 〈 |
|
〉 |
