收稿日期: 2015-11-07
修回日期: 2016-01-07
网络出版日期: 2016-09-15
基金资助
国家自然科学基金（11471308）资助
Existence of a class HCMU metric on S2
Received date: 2015-11-07
Revised date: 2016-01-07
Online published: 2016-09-15
魏志强 , 吴英毅 , 国金宇 . S2上一类HCMU度量的存在性[J]. 中国科学院大学学报, 2016 , 33(5) : 577 -583 . DOI: 10.7523/j.issn.2095-6134.2016.05.001
HCMU metric is an extremal Kähler metric with singularities on a compact Riemann surface. It is important to study the existence of HCMU metrics. Through studying the sufficient and necessary condition of Chen and Wu(Pacific J Math,2009,240(2):267-288) for the existence of HCMU metrics on S2, we show that there must exist a non-CSC HCMU metric on S2 which has N conical singularities and at least (N-1) saddle points.
Key words： extremal metric; compact Riemann surface; HCMU metric; conical singularity
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