Singular limits for thin film superconductors in strong magnetic fields

We consider singular limits of the three-dimensional Ginzburg-Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale epsilon > 0, and we consider the simultaneous limit as the thickness epsilon -> 0 and the Ginzburg-Landau parameter kappa -> Gamma infinity. We assume that the applied field is strong (on the order of epsilon(-1) in magnitude) in its components tangential to the film domain, and of order log kappa in its dependence on kappa. We prove that the Ginzburg-Landau energy Gamma-converges to an energy associated with a two-obstacle problem, posed on the planar domain which supports the thin film. The same limit is obtained regardless of the relationship between kappa and epsilon in the limit. Two illustrative examples are presented, each of which demonstrating how the curvature of the film can induce the presence of both (positively oriented) vortices and (negatively oriented) antivortices coexisting in a global minimizer of the energy.