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.
Correggi, M., & Rougerie, N. (2016). Effects of Boundary Curvature on Surface Superconductivity. LETTERS IN MATHEMATICAL PHYSICS, 106(4), 445-467 [10.1007/s11005-016-0824-z].