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中国科学院大学学报 ›› 2016, Vol. 33 ›› Issue (6): 721-728.DOI: 10.7523/j.issn.2095-6134.2016.06.001

• 数学与物理学 •    下一篇

Riemann面上带cusp奇点的共形度量

国金宇, 吴英毅, 魏志强   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2016-01-29 发布日期:2016-11-15
  • 通讯作者: 国金宇,E-mail:guojinyu14@163.com
  • 基金资助:

    国家自然科学基金面上项目(11471308)资助

Conformal metrics on Riemann surfaces with cusp singularities

GUO Jinyu, WU Yingyi, WEI Zhiqiang   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2016-01-29 Published:2016-11-15

摘要:

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

Abstract:

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

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