  We prove a $\Gamma$-convergence result for a class of Ginzburg-Landau type
functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is a closed
and $(k-2)$-connected submanifold of $\mathbb{R}^m$, 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 $\pi_{k-1}(\mathcal{N})$) which solves the Plateau
problem in codimension $k$. The analysis relies crucially on the set of
topological singularities, that is, the operator $\mathbf{S}$ we introduced in
the companion paper arXiv:1712.10203.
