We prove a \(\varGamma \)-convergence result for a class of Ginzburg–Landau type functionals with \({\mathscr {N}}\)-well potentials, where \({\mathscr {N}}\) 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 \(\pi _{k-1}({\mathscr {N}})\)) 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 [17].

我们证明了一类具有\({\mathscr {N}}\)阱势的 Ginzburg-Landau 型泛函的 \(\varGamma \) -收敛结果 ，其中 \({\mathscr {N}}\)是\({\mathbb {R}}^m\)的封闭和\((k-2)\)连接子流形 ，在任意维度。此类包括，例如，用于向列液晶的朗道-德热内斯自由能。受狄利克雷边界条件约束的极小分子的能量密度收敛到一个广义表面（更准确地说，是系数为\(\pi _{k-1}({\mathscr {N}})\)的扁平链 ），其中解决了k维中的高原问题 . 该分析主要依赖于拓扑奇点集，即我们在配套论文 [17] 中介绍的算子 \({\mathbf {S}}\)。