子流形几何是整体微分几何的重要研究内容，其研究不仅在几何分析等方面有重要作用，而且在理论物理等其它学科有很多应用。本项目主要研究与曲率流有关的几类子流形问题，包括：研究欧氏空间中紧致凸超曲面的Gauss曲率流和高维Firey猜想，即欧氏空间中紧致凸超曲面在高斯曲率流下唯一收敛到球面；研究欧氏空间中紧致凸超曲面的Gauss曲率的幂次流和广义Firey猜想；研究空间形式中超曲面的高阶曲率流及其收敛性和唯一性；通过研究双曲空间中超曲面的逆曲率流，建立最优Alexandrov-Fenchel型不等式；研究高维Willmore子流形，广义Willmore猜想和高维Willmore流。

Geometry of submanifolds is an important research branch of global differential geometry, it plays important roles in geometric analysis and some other fields in mathematics, it also has many applications in theoretic phyiscs and some other subjects. In this project, we will study some classes of problems of submanifolds related to curvature flows, which include: we will study the Gauss curvature flow for compact convex hypersurface in Euclidean space and the Firey Conjecture in higher dimension, i.e., any compact convex hypersurface in Euclidean space will converge to a round sphere under Gauss curvature flow; we will study the flow by powers of the Gauss curvature for compact convex hypersurface in Euclidean space and the generalized Firey Conjecture; we will study the convergence and uniqueness of the curvature flow of higher order for the hypersurfaces in space forms; we will establish some Alexandrov-Fenchel type inequalities by exploring the inverse curvature flow for hypersurfaces in hyperbolic space; we will study the Willmore submanifolds in higher dimension, the generalized Willmore Conjecture and Willmore flow in higher dimension.