澳门新葡官网进入2024 第11 期 数理大讲堂

主讲人：赵恩涛 教授（浙江大学）

主持人： 许洪伟教授（浙江大学）

讲座时间：2024年4月10日下午14:30-15:20

讲座地点：阿外楼酒店报告厅

讲座题目：The mean curvature flow and eigenvalue problems on submanifolds

摘要： In this lecture, we mainly discuss the mean curvature flow and eigenvalue problems on submanifolds. In particular, we present the following theorems obtained by our research team: (1) an optimal convergence theorem for higher codimensional mean curvature flow with positive Ricci curvature in hyperbolic space. Contrast to the famous sphere theorems due to Perelman and Cheeger-Colding, our result implies the first optimal differentiable sphere theorem for submanifolds with positive Ricci curvature; (2) a smooth convergence theorem for higher codimensional mean curvature flow in Riemannian manifolds under certain curvature pinching condition, which is an extension of the classical convergence theorem for mean curvature flow of hypersurfaces due to Huisken; (3) a generalized Li-Yau inequality for minimal submanifolds in Cartan-Hadamard manifolds with arbitrary codimension, which provides a strong evidence for that the generalized Pólya conjecture is true.