Abstract

By a classical result of Douglas, for any given $p\geq 0$ and configuration $\Gamma\subset \mathbb{R}^n$ of disjoint Jordan curves there exists an area minimizer among all compact surfaces of genus at most $p$ which span $\Gamma$. In the talk we will discuss a generalization of this theorem to singular configurations $\Gamma$ of possibly non-disjoint or self-intersecting curves. Furthermore, the talk will contain new existence results for regular configurations $\Gamma$ in more general ambient spaces such as Riemannian manifolds.

This is joint work with M. Fitzi.