Existence of multiply connected surfaces minimizing parametric integrals

Matthias Kurzke, IMA

We consider parametric integrals that can be seen as anisotropic and less smooth versions of the area functional. For these functionals, we prove existence of multiply connected minimizers spanned into a system of disjoint Jordan curves under a "Douglas condition", using a technique due to Courant. To obtain sufficient regularity and compactness we use a regularizing perturbation ("conformal approximation") that allows us to construct a good minimizing sequence.

This is joint work with Heiko von der Mosel, from our article "The Douglas problem for parametric double integrals", manuscripta mathematica 110, 93-114 (2003).