S2上一类HCMU度量的存在性 |
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作者姓名: | 魏志强 吴英毅 国金宇 |
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作者单位: | 中国科学院大学数学科学学院, 北京 100049 |
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基金项目: | 国家自然科学基金(11471308)资助 |
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摘 要: | HCMU度量是紧黎曼面上带奇点的extremal度量.研究它的存在性十分重要.通过研究Chen和Wu(Pacific J Math,2009,240(2):267-288)给出的S2上HCMU度量存在的充分必要条件,证明当S2上至少有(N-1)个鞍点时,一定存在non-CSC HCMU度量,其中N是所有锥奇点的个数.
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关 键 词: | 极值度量 紧黎曼面 HCMU度量 锥奇点 |
收稿时间: | 2015-11-07 |
修稿时间: | 2016-01-07 |
Existence of a class HCMU metric on S2 |
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Authors: | WEI Zhiqiang WU Yingyi GUO Jinyu |
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Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | 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. |
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Keywords: | extremal metric compact Riemann surface HCMU metric conical singularity |
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