MiS Preprint Repository

Let $\mathcal{F}$ be a parametric variational double integral and $\mathrm{\Gamma }\subset R^n$ be a system of distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers of $\mathcal{F}$ by solving the Douglas problem for parametric functionals on multiply connected schlicht domains. As a by-product we obtain a simple isoperimetric inequality for multiply connected $\mathcal{F}$-mimimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau problem.