Let be a three-dimensional Riemannian manifold and let be some surface of prescribed mean curvature which is restricted to lie in some set with boundary of bounded mean curvature . Assuming natural conditions, we prove that the image of lies completely in . An immediate consequence of this result is a sufficient condition for the existence of minimal surfaces in a set , the boundary of which is not -convex.
Cite this article
Ulrich Dierkes, A Geometric Maximum Principle for Surfaces of Prescribed Mean Curvature in Riemannian Manifolds. Z. Anal. Anwend. 8 (1989), no. 2, pp. 97–102DOI 10.4171/ZAA/340