曲率流的奇点几何结构及相关问题

曲率流的奇点几何结构问题是微分几何和几何分析领域中的一个重要课题，因为对奇点结构的研究，可以澄清子流形几何中的许多重要问题。目前，仍有很多关于奇点的基本问题是不清楚的。.综上可知，奇点几何结构及相关问题是非常有意义且重要的研究课题。本项目拟在已有工作基础上，重点对曲率流的奇点几何结构及相关问题展开研究。研究内容分三部分：（1）研究平均曲率流的奇点self-shrinkers的分类问题和刚性问题；（2）研究entropy的刚性问题；（3）研究$\lambda$-超曲面的分类问题和刚性问题。

Geometric structures of singularities of curvature flows are very interesting and important problems in the fields of differential geometry and geometry analysis because one can know some important properties of submanifolds. At present, one can not know some of the basic properties about the singularities.. From the above arguments, we know that it is very interesting and important to study geometric structures of singularities and related problems. Based on previous work, in this project, we are going to investigate geometric structures of singularities of curvature flows and related problems. Specifically, we will try to study: (1) Classification and rigidity of self-shrinkers of mean curvature flow; (2)The rigidity of entropy; (3) Classification and rigidity of $\lambda$- hypersurfaces.