  It is a well known fact that the geometry of a superconducting sample
influences the distribution of the surface superconductivity for strong applied
magnetic fields. For instance, the presence of corners induces geometric terms
described through effective models in sector-like regions. We study the
connection between two effective models for the offset of superconductivity and
for surface superconductivity introduced in \cite{BNF} and \cite{CG2},
respectively. We prove that the transition between the two models is continuous
with respect to the magnetic field strength, and, as a byproduct, we deduce the
existence of a minimizer at the threshold for both effective problems.
Furthermore, as a consequence, we disprove a conjecture stated in \cite{CG2}
concerning the dependence of the corner energy on the angle close to the
threshold.
