Global and Exterior Solutions to the Minimal Surface Equation

报告人：韩青（美国圣母大学）

时  间：2026年6月18日10:00

地  点：海韵园行政楼C802

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.

个人简介：

韩青，美国圣母大学数学系终身教授。美国纽约大学库朗数学研究所博士，美国芝加哥大学博士后。获美国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，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。

联系人：宋翀