几何分析讨论班

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）

时  间：2026年7月10日（星期五），下午16:00-17:00

地  点：海纳苑2幢204

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.