Enhanced cohesion of matter on a cylindrical surface

We evaluate the cohesive energies (formula presented) of four systems in which particles move on a cylindrical surface, at fixed distance R from the axis. We find quite nonuniversal dependences of (formula presented) on R. For the Coulomb binding problem, (formula presented) is a monotonically decreasing function of R. For three problems involving Lennard-Jones interactions, the behavior is nonmonotonic; (formula presented) is larger at (formula presented) than at (formula presented) The maximum binding corresponds to (formula presented) where (formula presented) is the hard core parameter. Consequences of the enhanced binding are discussed.