Stability of Capillary Hypersurfaces with Planar Boundaries

Abstract

We prove that, in a Euclidean domain bounded by hyperplanes having linearly independent normals, a connected oriented compact immersed stable capillary hypersurface Mn disjoint from the edges of the domain and with the contact angles belonging to [π/2,π] must be part of a sphere, if ∂M is embedded for n=2, or ∂M is convex in the hyperplane for n≥3. By applying a similar argument, we also discuss two other cases where a stable capillary hypersurface must be part of a sphere. Show more