Mean-convex sets and global barriers to minimal hypersurfaces

Emanuele Spadaro (MPI Leipzig)

In this talk I will present some results about the relations
between mean-convex sets and global supersolutions to the Plateau problem.
We will show that these two notions do not coincide in any reasonable
sense. Then, starting from this, we will characterize the least global
barrier to minimal hypersurfaces with boundary on a given set of
$\mathbb{R}^n$, $n\leq 7$, in terms of a constrained mean curvature flow
with obstacle.