Global and Exterior Solutions to the Minimal Surface Equation

Speaker：Qinghan (University of Notre Dame du Lac)

Time：2026-6-18 10:00

Location：Conference Room C802 at Administration Building at Haiyun Campus

Abstract:

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.