Uniqueness for certain surfaces of prescribed mean curvature (Q1089966)

This paper deals with a problem which arises naturally from the classical problem of the shape of the free surface of a liquid in a capillary tube. The usual approach has been to consider absolute minima of the relevant energy functional, to show that an absolute minimum has a free surface which is the graph of a function satisfying a nonlinear partial differential equation, and to then apply uniqueness theorems for such functions. The present paper weakens these hypotheses by considering relative minima (in the setting of BV theory) and stationary points (in a classical differential geometry setting). In both cases the surface has prescribed mean curvature which is nondecreasing with height, and satisfies a contact angle condition. Under these weakened hypotheses, uniqueness still holds, so that no new surfaces are found.