The Jacobian and the Ginzburg-Landau energy

We show that if the Ginzburg-Landau energy is uniformly bounded for a sequence of functions u_ε as ε → 0, then the Jacobians {Ju_ε} are precompact in a ppropriate weak topologies. We further show that any limiting measure must be rectifiable. These results have potential applications in problems a variety of problems, including for example questions involving dynamics of vortex filaments in superfluids. (joint work with Mete Soner)