在S^2或T^2上HCMU的曲率的光滑性(英文)  

Smoothness of the curvature of an HCMU on S^2 or T^2

作　　者：吴英毅[1] 

机构地区：[1]中国科学院研究生院数学学院,北京100049

出　　处：《中国科学院研究生院学报》2008年第5期585-591,共7页Journal of the Graduate School of the Chinese Academy of Sciences

摘　　要：HCMU是一种在Riemann面上带奇点的extremal度量.在面积和Calabi能量有界的情况下,HCMU的Gauss曲率是Riemann面上的连续函数.本文得到一个在球面上没有Gauss曲率鞍点的HCMU的明显表达式,并进一步证明了在球面或环面上HCMU的Gauss曲率光滑的充要条件是度量的所有奇点的角度都是整数.An HCMU is a kind of extremal metric with singularities on a Riemann surface. If the area and the Calabi energy are both bounded, the Gauss curvature of an HCMU is a continuous function on the Riemann surface. In this paper we get an explicit construction of an HCMU on S^2 which has no saddle point of the Gauss curvature of the metric. Further more we prove that on S^2 or T^2 the Gauss curvature of an HCMU is smooth if and only all of the singular angles are integers.

关 键 词：extremal度量 HCMU 锥奇点 奇角度 

分 类 号：O186.1[理学—数学]