Stability of Capillary Hypersurfaces with Planar Boundaries

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.