  We investigate, within 2D Ginzburg-Landau theory, the ground state of a
type-II superconducting cylinder in a parallel magnetic field varying between
the second and third critical values. In this regime, superconductivity is
restricted to a thin shell along the boundary of the sample and is to leading
order constant in the direction tangential to the boundary. We exhibit a
correction to this effect, showing that the curvature of the sample affects the
distribution of superconductivity.
