Ricerc@Sapienza

This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by the length scale parameter in such models, we focus on the |log | energy regime. It is well known that, for configurations whose energy is bounded by c|log |, the vorticity measures can be decoupled into the sum of a finite number of Dirac masses, each one of them carrying I|log | energy, plus a measure supported on small zero-average sets.