本项目是有关Kaehler-Ricci孤立子和Kaehler-Ricci流的研究。Kaehler-Ricci孤立子和Kaehler-Ricci流的研究是复几何研究的热点课题。(Kaehler-)Ricci流的研究是当今几何分析的一大热点，由于Kaehler-Ricci孤立子即可以看成Kaehler-Einstein度量的推广，也可以看成是Ricci流的奇异模型，因此它的研究也是当今几何分析的一大热点。Kaehler-Ricci流是研究Kaehler-Einstein度量和Kaehler-Ricci孤立子的非常重要的工具。围绕Kaehler-Ricci孤立子和Kaehler-Ricci流，我们将集中以下三个方面的问题，即有关Kaehler-Ricci流的Hamilton-田刚猜想，Kaehler-Ricci孤立子的稳定性，及复曲面上完备非紧Kaehler-Riccci孤立子的分类问题。

This research project is about the study of the Kaehler-Ricci solitons and the Kaehler-Ricci flow. The study of the Kaehler-Ricci solitons and the Kaehler-Ricci flow is one of hot problems in complex geometry. (Kaehler-)Ricci flow is a big hot topic in geometric analysis, Kaehler-Ricci soltions as the generalization of Kaehler-Einstein metrics, also as the singularity modle of the Kaehler-Ricc flow, is also a hot topic in geometric analysis. Kaehler-Ricci flow is a very important tool in the study of Kaehler-Einstein metrics and the Kaehler-Ricci solitons. In our project, we will study the folowing 3 problems: 1)Hamilton-Tian's conjecture in Kaehler-Ricci flow; 2) the stability problem of the Kaehler-Ricci solitons; 3) the classification of the complete noncompact Kaehler-Ricci solitons for complex suface.