On the regularity of minimal surfaces with free boundaries in Riemannian manifolds

We show c^1,-regularity of minimal surfaces in Riemannian manifolds with a free boundary on C²-hypersurfaces with bounded second fundamental form and a uniform neighborhood on which the nearest point projection is uniquely defined and differentiable. The decisive step is the proof of continuity at the free boundary.partially supported by SFB 72 (Deutsche Forschungsgemeinschaft)