Plateau's problem in infinite-dimensional spaces

Thomas Schmidt (Hamburg)

Abstract: The classical Plateau problem consists in finding a surface
of minimal area among all 2-dimensional surfaces with a prescribed
boundary curve in Euclidean 3-space. This problem can be reformulated
for non-smooth oriented surfaces of arbitrary finite dimension, known
as currents, and then makes sense in a very general ambient space. The
talk will start with an introduction to (metric) currents and will
then report on existence and regularity results for current solutions
of the Plateau problem in an infinite-dimensional Banach or Hilbert
space. These results have been obtained in collaboration with L.
Ambrosio and C. De Lellis.