We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
30/2002
The Douglas problem for parametric double integrals
Matthias Kurzke and Heiko von der Mosel
Abstract
Let $\mathcal{F}$ be a parametric variational double integral and $\Gamma\subset R^n$ 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.