报告题目：Global and Exterior Solutions to the Minimal Surface Equation

报 告 人：韩青教授（美国圣母大学University of Notre Dame）

报告时间：2026年3月10日  15:00

报告地点：格物楼528

报告摘要：

Acharacterization 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.

报告人简介：

韩青，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原创性的重要研究成果。在《Duke Math. J.》《Comm. Pure Appl. Math.》《Geom. Funct. Anal.》《J. Differ. Geom.》《Crelle's Journal》等权威学术杂志上发表70余篇科研论文。