Topological Singular Set of Vector-Valued Maps, II: Gamma-convergence for Ginzburg-Landau type functionals

We prove a Gamma-convergence result for a class of Ginzburg-Landau type functionals with N-well potentials, where N (is a closed and (k - 2)-connected submanifold of R-m, in arbitrary dimension. This class includes, for instance, the Landau-de Gennes free energy for nematic liquid crystals. The energy density of minimisers, subject to Dirichlet boundary conditions, converges to a generalised surface (more precisely, a flat chain with coefficients in pi(k-1) (N)) which solves the Plateau problem in codimension k. The analysis relies crucially on the set of topological singularities, that is, the operator S we introduced in the companion paper [17].