A complete wetting transition at vanishing curvature of the substrate in two-dimensional circular geometry is studied by the transfer matrix method. We find an exact formal mapping of the partition function of the problem onto that of a (l+l)-dimensional wetting problem in planar geometry. As the radius of the substrate ro -> oo, the leading effect of the curvature is adding the Laplace pressure JIL oc r_0~(-1/3). to the pressure balance in the film. At temperatures and pressures under which the wetting is complete in planar geometry, Laplace pressure suppresses divergence of the mean thickness of the wetting layer lw, leading to a power law lw oc r_0~(-1/3). At a critical wetting transition of a planar substrate, curvature adds a relevant field; the corresponding multiscaling forms are readily available. The method allows for the systematic evaluation of corrections to the leading behavior; the next to the leading term reduces the thickness by an amount proportional r_0~(-1/3).
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