学术报告(李文俊 11.09)

Mean curvature flow with free boundary (带自由边界的平均曲率流)

发布人:杨晓静 发布日期:2019-10-31
主题
Mean curvature flow with free boundary (带自由边界的平均曲率流)
活动时间
-
活动地址
数学楼403讲学厅
主讲人
李文俊助理教授 香港中文大学数学系

时间:2019年11月9日下午2点至3点

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 an- alytic 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 im- posed to ensure the evolution equations are well-posed. Two such boundary conditions are the Dirichlet (fixed or prescribed) and Neumann (free or prescribed contact an- gle) boundary conditions. We will mention some new phenomena in contrast with the classical MCF without boundary. We give a convergence result for mean curvature flow of convex hypersurfaces with free boundary. This is joint work with Sven Hirsch. (These works are partially supported by RGC grants from the Hong Kong Government.)