活动时间：2026-06-26 10:30
活动地点：2号学院楼2432
主讲人：韩青
主讲人简介：
韩青教授本科毕业于北京大学，在美国纽约大学柯朗数学研究所获得博士学位，现为美国圣母大学数学系终身教授。曾入选国家级海外高层次人才计划以及美国Sloan Research Fellowship。韩青教授长期致力于非线性偏微分方程和几何分析的研究工作，在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程等方面做出了一系列重要的原创性工作；相关工作发表在《Duke Math. J.》、《Comm. Pure Appl. Math.》、《Geom. Funct. Anal.》、《J. Differ. Geom.》、《Crelle's Journal》等学术期刊上。
内容摘要：
A characterization of global solutions to the minimal surface equation has been known by the efforts of Bernstein (1914), De Giorgi (1965), Almgren (1966), Simons (1968), and Bombieri, De Giorgi, and Giusti (1969). In this talk, we first review relevant results. Then, we switch to exterior solutions and aim to present a complete characterization of solutions to the minimal surface equation near infinity. It is well-known that Dirichlet boundary value problems in exterior domains do not always admit solutions. We demonstrate that prescribing asymptotic behaviors forms a new type of problems leading to all solutions near infinity. The harmonic functions determining the asymptotic behaviors play the role of “free data” as the boundary values in the boundary value problems.
主持人：孙春友