  We examine the hydrodynamic phonon spectrum of a monolayer film adsorbed on
the wall of a spherical pore. Due to the boundary conditions, the monolayer
film exhibits a discrete phonon spectrum. The corresponding density of states
per unit frequency is thus a set of delta functions and the heat capacity
exhibits Arrhenius behavior at low temperatures. At high temperatures, the heat
capacity approaches the C ~ T^2 behavior of a two-dimensional monolayer film.
Our results for the spherical surface film are compared to previous
calculations for films confined to a cylindrical surface.
