  We evaluate the cohesive energies E$_b$ of four systems in which particles
move on a cylindrical surface, at fixed distance R from the axis. We find quite
nonuniversal dependences of E$_b$ on R. For the Coulomb binding problem, E$_b$
is a monotonically decreasing function of R. For three problems involving
Lennard-Jones interactions, the behavior is nonmonotonic; E$_b$ is larger at R
= $\infty$ than at R=0; the maximum binding corresponds to R $\sim 0.7 \sigma$
(the hard core parameter). Consequences of the enhanced binding are discussed.
