本项目拟研究几何中的极值凯勒度量与几何曲率流相关问题。凯勒几何中的极值凯勒度量和卡拉比流相关问题在过去几十年中一直是几何中的热点研究问题。我们希望研究卡拉比流的长时间存在性，与收敛性有关的Donaldson猜想，以及卡拉比流, 能量泛函和极值凯勒度量存在性之间的关系。此外，对于欧式空间中的平均曲率流，我们希望研究不假设凸性条件下平均曲率流的长时间存在性，奇点性质以及平均曲率流自相似解的性质，同时将发展出的方法应用于拉格朗日平均曲率流, 最终希望对Thomas-Yau猜想有所突破。

In this program we will study extremal Kahler metrics in Kahler geometry and geometric evolution equations. The topics on extremal Kahler metrics and Calabi flow have been intensively studied during the past several decades. We will study the long time existence, the convergence of the Calabi flow(Donaldson conjectures), and the relations between Calabi flow, energy functionals and the existence of extremal Kahler metrics. Moreover, for the mean curvature flow in the Euclidean space we will study the long time existence, the properties of the singularities and the self-similar solutions. We hope to develop some methods which can be applied to Lagrangian mean curvature flow and Thomas-Yau conjecture.