Smoothness of the curvature of an HCMU on S2 or T2
在S2或T2上HCMU的曲率的光滑性

An HCMU is a kind of extremal metric with singularities on a Riemann surface. If the area and 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 S2 which has no saddle point of the Gauss curvature of the metric. Further more we prove that on S2 or T2 the Gauss curvature of an HCMU is smooth if and only all of the singular angles are integers.