We prove that every non‐degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg–Landau functional. The proof is purely variational, and follows the strategy laid out by Jerrard and Sternberg, extending a recent result for geodesics by Colinet–Jerrard–Sternberg. The same proof applies also to the ‐Yang–Mills–Higgs and to the Allen–Cahn–Hilliard energies. While for the latter energies gluing methods are also effective, in general dimension our proof is by now the only available one in the Ginzburg–Landau setting, where the weaker energy concentration is the main technical difficulty.

中文翻译：

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作为能量集中集的非简并最小子流形：变分方法

我们证明，余维二的每个非简并最小子流形都可以作为（重新缩放的）Ginzburg-Landau 泛函的一系列临界图的能量集中集来获得。该证明纯粹是变分的，遵循杰拉德和斯滕伯格提出的策略，扩展了科林特-杰拉德-斯滕伯格最近的测地线结果。同样的证明也适用于杨-米尔斯-希格斯能量和艾伦-卡恩-希利亚德能量。虽然对于后一种能量粘合方法也是有效的，但在一般维度上，我们的证明是迄今为止在金茨堡-兰道环境中唯一可用的证明，其中较弱的能量集中是主要的技术困难。