Xiaoding Yang will give a talk at 11/19/2024.

The problem of finding the surface of least area among those bounded by a given curve, which is the so-called minimal surface problem or Plateau problem, was one of the first considered after the foundation of the calculus of variations. And this problem has received a satisfactory solution only in recent years. If our surface is restricted to be a graph of a function $u(x)$ defined in some open set, then we call it the non-parametric minimal surface. In this talk, I will first give an introduction which is related to my recent research on the contact line problem. Then I will show the classical barrier function method to get the minimizer of the area functional in the non-parametric minimal surface problem.