Multi-valued holomorphic functions and non-CSC extremal Kahler metrics with singularities on compact Riemann surfaces

作者：Wei, Zhiqiang; Wu, Yingyi^*

来源：Differential Geometry and its Applications, 2018, 60: 66-79.

DOI：10.1016/j.difgeo.2018.05.008

• Extremal Kahler metric
• HCMU metric
• Multi-valued holomorphic function
• Monodromy group

An extremal Kahler metric with finite singularities on a compact Riemann surface is often called an HCMU metric. It can be regarded as a generalization of CSC (constant scalar curvature) metric. In this paper we will prove that any HCMU metric is a pullback of an HCMU metric on S-2 with only two singularities (we call it football) by a multi-valued holomorphic function. Then we study the monodromy group of the multi-valued function.

• 出版日期2018-10
• 单位中国科学院大学; 河南大学