I will show that every non-degenerate minimal sub-manifold of codimension 2 can be obtained as the energy concentration set of a family of critical points of the (rescaled) Ginzburg Landau functional. The proof is purely varia-tional, and follows the strategy laid by Jerrard and Sternberg in 2009. The same proof applies also to the Yang-Mills-Higgs and to the Allen-Cahn-Hillard energies.

This is a joint work with Alessandro Pigati.