  We study the superconducting properties of a two-dimensional superconductor
in the proximity to an electronic topological transition (ETT). In contrast to
the 3D case, we find that the superconducting gap at T=0, the critical
temperature Tc, and the impurity scattering rate are characterized by a
nonmonotonic behavior, with maxima occurring close to the ETT. We derive
analytical expressions for the value of such maxima both in the s-wave and in
the d-wave case. Such expressions are in good qualitative agreement with the
phenomenological trend recently observed for Tc^max as a function of the
hopping ratio t'/t across several cuprate compounds. We further analyze the
effect of an ETT on the Ginzburg-Landau stiffness eta. Instead of vanishing at
the ETT, as could be expected, thus giving rise to an increase of the
fluctuation effects, in the case of momentum-independent electron-electron
interaction, we find eta different from 0, as a result of an integration over
the whole Fermi surface.
