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Static equilibrium configurations of continua supported by surface tensionare given by constant mean curvature (CMC) surfaces which are critical pointsof 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 astiny liquid drops, stars, and nuclei, to play important roles in bothmathematics and physics. Therefore, the geometry of CMC surfaces and theirproperties such as stability are of special importance in differential geometryand in a variety of physical sciences. In this paper we examine the stabilityof CMC hypersurfaces in arbitrary dimensions, possibly having boundaries on twoparallel hyperplanes, by investigating the second variation of the area. Wedetermine the stability of non-uniform liquid bridges or unduloids for thefirst time in all dimensions and all parameter (the ratio of the neck radius tobulge radius) regimes. The analysis is assisted by numerical computations.

Stability of hypersurfaces with constant mean curvature trapped between two parallel hyperplanes