Kahler几何中的极值度量是当今国内外的研究热点。我们研究Kahler曲面上极值度量若干问题，内容包括：研究带角度极值度量的存在性、唯一性；构造Kahler曲面极值度量的典型实例；研究极值度量的几何拓扑性质；研究极值度量的形变和Extremal Soliton存在性等问题。希望得到复射影面上带角度极值度量的分类、Kahler曲面上一般极值度量构造法、极值度量存在的几何拓扑障碍等结论，给出极值度量可形变条件、Kahler曲面上带角度极值度量存在唯一的条件。通过解决这些问题，人们有望得到对Kahler曲面极值度量一个系统深入的了解。

We study the extremal metric on Kahler surface, which is the critical point of Calabi functional of a Kahler class. The research topic includes:construction of typical extremal metrics, geometric-topological properties of extremal metrics,deformation of extremal metrics and existence of extremal solitons. We are going to obtain following results: the classification of extremal metrics on CP^2 with conical singularities, the geometric-tological obstruction of the existence of extremal metrics,the condition of deformations of extremal metrics,existence and uniqueness of extremal metrics with conical sinularities, etc.It is expected to understand extremal matrics on Kahler surfaces by studying these problems.