学术报告：Overdetermined problem for minimal surface equation

报告人：崔庆

报告时间：2021年11月16日下午3:00-4:00

报告地点：腾讯会议：689724789

报告题目：Overdetermined problem for minimal surface equation

报告人简介：崔庆，西南交通大学，副教授。本科毕业于华中师范大学，2010年博士毕业于武汉大学，主要从事子流形几何研究。具体研究兴趣为：常平均曲率曲面，第二基本形式模长夹击定理，特征值估计，四维Einstein流形和子流形等问题。主持过一项国家自然科学基金青年基金，参与国家自然科学基金若干项。已在Calc. Var. Partial Differential Equations, J. Differential Equations等国际数学期刊上发表论文9篇。

报告摘要：In this talk, we will first summarize some developments of overdetermined problems for Poisson equations. Then we will give a rigidity result of overdetermined problem for minimal surface equation. More precisely, we will show that an overdetermined problem over a domain $\Omega \subset R^2$ with connected boundary has a $C^2$ solution if and only if $\Omega$ is the complement of a round disk or a half plane.  Equivalently, we show that a minimal graph defined over a domain $\Omega \subset R^2$ with connected boundary and makes a constant angle with $\Omega$ along the boundary must be a part of a catenoid or a half plane.