Résume  Plateau’s problem is one of the central problems in Geometric Analysis and PDE.
Given an arbitrary closed curve in R3, it asks for the existence of an area minimizing
embedded surface with boundary equal to the given curve.
In 1960, Federer and Fleming conceived the theory of currents as a framework for
solving this problem. A different approach was proposed in 1990 by Fröhlich and
Struwe, through the study of level sets of semilinar elliptic equations. They showed
the existence of a minimal surface which was smooth far away from the curve.
I will talk about joint work with Stephen Lynch, in which we show that the surface is
also smooth up to the boundary, thus completing a new solution to Plateau’s problem.
