## Existence of multiply connected surfaces minimizing parametric integrals

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Matthias Kurzke, *IMA
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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).