Topological Singular Set of Vector-Valued Maps, II: $$\varGamma $$-convergence for Ginzburg–Landau type functionals

We prove a $\Gamma$-convergence result for class of Ginzburg-Landau type functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is closed and $(k-2)$-connected submanifold $\mathbb{R}^m$, in arbitrary dimension. This includes, instance, the Landau-de Gennes free energy nematic liquid crystals. The density minimisers, subject to Dirichlet boundary conditions, converges generalised surface (more precisely, flat chain coefficients $\pi_{k-1}(\mathcal{N})$) which solves Plateau problem codimension $k$. analysis relies crucially on set topological singularities, that is, operator $\mathbf{S}$ we introduced companion paper arXiv:1712.10203.