Marco Guaraco (Imperial College London)

Solving Plateau's problem via semilinear elliptic equations

Abstract:

The smooth version of Plateau's problem is to show the existence of a regular minimal surface with any given smooth boundary curve in ℝ³. Historically, studying problems of this type required the framework of Geometric Measure Theory, e.g. the theory of currents. However, I will discuss how new techniques allow us to tackle this and other problems with usual tools from Analysis and PDE, in particular, via understanding the level set regularity of solutions to semilinear elliptic equations. This is joint work with Stephen Lynch.