On the existence of minimal surfaces with singular boundaries

In 1931, Jesse Douglas showed that in $\mathbb {R}^{n}$, every set of $k$ rectifiable Jordan curves, with $k \ge 2$, bounds an area-minimizing minimal surface with prescribed topological type if a ``condition of cohesion'' is satisfied. In this paper, it is established that under similar conditions, this result can be extended to non-Jordan curves.