  The thickness $W$ and the surface energy $\sigma_A$ at the free interface of
superfluid $^4$He are studied. Results of calculations carried out by using
density functionals for cylindrical and spherical systems are presented in a
unified way, including a comparison with the behavior of planar slabs. It is
found that for large species $W$ is independent of the geometry. The obtained
values of $W$ are compared with prior theoretical results and experimental
data. Experimental data favor results evaluated by adopting finite range
approaches. The behavior of $\sigma_A$ and $W \sigma_A$ exhibit overshoots
similar to that found previously for the central density, the trend of these
observables towards their asymptotic values is examined.
