Mean curvature flows with boundary
报告题目(Title)：Mean curvature flows with boundary
报告人(Speaker)：Li, Martin Man-chun （香港中文大学）
地点(Place)：后主楼1220室
时间(Time)：2019年6月25日17:00-18:00
邀请人(Inviter)：葛建全
报告摘要
Mean curvature flow (MCF) is the negative gradient flow for the area functional in Euclidean spaces, or more generally in Riemannian manifolds. Over the past few decades, there have been substantial progress towards our knowledge on the analytic and geometric properties of MCF. For compact surfaces without boundary, we have a fairly good understanding of the convergence and singularity formation under the flow. In this talk, we will discuss some recent results on MCF of surfaces with boundary. In the presence of boundary, suitable boundary conditions have to be imposed to ensure the evolution equations are well-posed. Two such boundary conditions are the Dirichlet (fixed or prescribed) and Neumann (free or prescribed contact angle) boundary conditions. We will mention some new phenomena in contrast with the classical MCF without boundary and discuss some potential applications. These works are partially supported by RGC grants from the Hong Kong Government.
主讲人简介
李文俊2011年博士毕业于斯坦福大学，师从沃尔夫奖得主Richard Schoen教授，其后在英属哥伦比亚大学和MIT做过博士后。他主要研究几何分析特别是自由边界极小曲面问题，已在JDG,CPAM等顶级期刊发表多篇论文。
