Journal of Statistical Physics, Vol. 50, Nos. 3/4, 1988. p. 737-754.
A rigorous inequality is derived relating density gradient, interface thickness, transverse correlation length, and distance of the interface from the wall in the presence of an explicit gravitational (resp. wall potential). The results are relevant to various possible scenarios, e.g. (critical) wetting, drying, roughening, free interfaces (i.e., far away from a wall). Attention is concentrated on the structure of the liquid gas interface in a gravitational field. Results seem to indicate that the usual intuition concerning the fine structure of the liquid-gas interface (e,g., the capillary wave picture) cannot be entirely correct. The predictions are particularly puzzling in space dimension two. The results are physically interpreted, giving a more refined picture of the interface layer.