Abstract

Ginzburg-Landau type functionals provide a relaxation scheme to construct harmonic maps in the presence of topological obstructions. They arise in superconductivity models, in liquid crystal models (Landau-de Gennes functional) and in the generation of cross-fields in meshing. For a general compact manifold target space we describe the asymptotic number, type and location of singularities that arise in minimizers. We cover in particular the case where the fundamental group of the vacuum manifold is nonabelian and hence the singularities cannot be characterized univocally as elements of the fundamental group. We obtain similar results for $p$-harmonic maps with $p$ going to $2$. The results unify the existing theory and cover new situations and problems.

This is a joint work with Antonin Monteil (Paris-Est Créteil, France), Rémy Rodiac (Paris–Saclay, France) and Benoît Van Vaerenbergh (UCLouvain).