STABLE CAPILLARY HYPERSURFACES IN A WEDGE

Let Sigma be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in Rn+1. Suppose that Sigma meets those two hyperplanes in constant contact angles >= pi/2 and is disjoint from the edge of the wedge, and suppose that partial derivative Sigma consists of two smooth components with one in each hyperplane of the wedge. It is proved that if partial derivative Sigma is embedded for n = 2, or if each component of partial derivative Sigma is convex for n >= 3, then Sigma is part of the sphere. The same is true for Sigma in the half-space of Rn+1 with connected boundary partial derivative Sigma.