  Consider a closed lipid membrane (vesicle), modeled as a two-dimensional
surface, described by a geometrical hamiltonian that depends on its extrinsic
curvature. The vanishing of its first variation determines the equilibrium
configurations for the system. In this paper, we examine the second variation
of the hamiltonian about any given equilibrium, using an explicitly surface
covariant geometrical approach. We identify the operator which determines the
stability of equilibrium configurations.
