  We argue that for complete wetting at a curved substrate (wall) the
wall-fluid surface tension is non-analytic in $R_i^{-1}$, the curvature of the
wall and that the density profile of the fluid near the wall acquires a
contribution proportional to the gas-liquid surface tension $\times R_i^{-1}$
plus higher-order contributions which are non-analytic in $R_i^{-1}$. These
predictions are confirmed by results of density functional calculations for the
square-well model of a liquid adsorbed on a hard sphere and on a hard cylinder
where complete wetting by gas (drying) occurs. The implications of our results
for the solvation of big solvophobic particles are discussed.
