  Static equilibrium configurations of continua supported by surface tension
are given by constant mean curvature (CMC) surfaces which are critical points
of a variational problem to extremize the area while keeping the volume fixed.
CMC surfaces are used as mathematical models of a variety of continua, such as
tiny liquid drops, stars, and nuclei, to play important roles in both
mathematics and physics. Therefore, the geometry of CMC surfaces and their
properties such as stability are of special importance in differential geometry
and in a variety of physical sciences. In this paper we examine the stability
of CMC hypersurfaces in arbitrary dimensions, possibly having boundaries on two
parallel hyperplanes, by investigating the second variation of the area. We
determine the stability of non-uniform liquid bridges or unduloids for the
first time in all dimensions and all parameter (the ratio of the neck radius to
bulge radius) regimes. The analysis is assisted by numerical computations.
