  Type-II superconductivity is known to persist close to the sample surface in
presence of a strong magnetic field. As a consequence, the ground state energy
in the Ginzburg-Landau theory is approximated by an effective one-dimensional
model. As shown in [CG2], the presence of corners on the surface affects the
energy of the sample with a non-trivial contribution. In [CG2], the
two-dimensional model problem providing the corner energy is implicitly
identified and, although no explicit dependence of the energy on the corner
opening angle is derived, a conjecture about its form is proposed. We study
here such a conjecture and confirm it, at least to leading order, for corners
with almost flat opening angle.
