On a free boundary problem for minimal surfaces (Q792543)

For \(C^ 4\)-embedded manifolds \(S\subset {\mathbb{R}}^ 3\) which are diffeomorphic to the standard sphere in \({\mathbb{R}}^ 3\) the existence of non-constant minimal surfaces bounded by S and intersecting S orthogonally along their free boundaries is deduced. The proof uses an adaptation of a method devised by Sacks and Uhlenbeck for the study of harmonic mappings and a mountain-pass-type characterization of approximate solution surfaces.