Sufficient conditions for capillary surfaces to be energy minima

It is shown that if a capillary surface satis es conditions relating to the eigenvalues of a certain differential operator, then the surface is a constrained strict local minimum for the relevant energy functional. The space of perturbations of the surface is rst defined in terms of graphs of functions in curvilinear coordinates and then related to perturbations of capillary surfaces which are uniformly small and have uniformly small derivatives.