Topic: Global and Exterior Solutions to the Minimal Surface Equation

Lecturer: Han Qing, Professor at University of Notre Dame

Time: March 11th, 2026, 15:30, UTC+8

Venue: Room 209, Mathematics and Statistics Building

Biography: Han Qing is a tenured professor at the University of Notre Dame, USA. He holds a Ph.D. from the Courant Institute of Mathematical Sciences at New York University and completed postdoctoral research at the University of Chicago. He is a recipient of the Sloan Research Fellowship. He has long been dedicated to research in partial differential equations and geometric analysis, producing a series of original and significant results in areas such as isometric embedding, Monge-Ampère equations, zero sets and singular sets of harmonic functions, degenerate equations, singular equations, and blow-up problems. He has published over 40 high-level academic papers in internationally renowned journals, including Comm. Pure Appl. Math., J. Differential Geom., and Comm. Partial Differential Equations, with citations exceeding 500 times. He has also authored more than three related books.

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.

Rewritten by: Li Huihui

Edited by: Li Tiantian

Source: School of Mathematics and Statistics