本项目主要研究Kahler曲面中的特殊曲面。 这些曲面是高余维的，分析上更困难。具体地， （1）Kahler 曲面中全纯曲线的存在性。我们将试图利用分析的方法来研究全纯曲线的存在性。为此我们将研究我们最新构造的泛函以及相对应的几何流。Siu-Yau 证明了Sacks-Uhlenbeck得到的极小球面在某些情况下是全纯的。我们将进一步研究极小曲面与全纯曲线的关系。 （2）高余维平均曲率流。我们将着重研究高余维平均曲率流奇点的性质，特别是自相似解和translating soliton， 并应用这些结果到Lagrangian和辛平均曲率流来寻找Lagrangian 和辛极小曲面。 （3）另外，我们也将研究Moser-Trudinger泛函对应的热流方程。主要研究这个方程的长时间存在性与序列紧性。 这些问题涉及到椭圆型、抛物型方程， 调和分析， 几何测度论等多个领域。这些问题的研究有趣且重要。

This project is going to consider the special surfaces in Kahler surface and these surfaces are codimension two. (1) the existence of the holomorphic curves in Kahler surface. In order to study the holomorphic curves we will study our new functional. Siu-Yau have proved that the minimal sphere which Sacks-Uhlenbeck got is holomorphic. Furthermore, we will study the relationship between the minimal surface and the holomorphic curve. （2）the mean curvature flow in higher codimension. We will study the singularities, especially the similar solution and the translating soliton. We will apply these results to the Lagrangian mean curvature flow and symplectic mean curvature flow. (3) the heat equation which comes from the Moser-Trudinger functional. These problems include the elliptic and parabolic equations, harmonic analysis, geometric measure and so on. These problems are intresting and important.