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›› 2016, Vol. 33 ›› Issue (5): 577-583.DOI: 10.7523/j.issn.2095-6134.2016.05.001

• Research Articles •     Next Articles

Existence of a class HCMU metric on S2

WEI Zhiqiang, WU Yingyi, GUO Jinyu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-11-07 Revised:2016-01-07 Online:2016-09-15

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.

Key words: extremal metric, compact Riemann surface, HCMU metric, conical singularity

CLC Number: