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On solutions to the Ginzburg-Landau equations in higher dimensions

Simon Brendle
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Abstract

We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau equations such that the energy density concentrates near this submanifold. The proof is based on a construction of suitable approximate solutions and the implicite function theorem.

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Simon Brendle. 2003-08-13. On solutions to the Ginzburg-Landau equations in higher dimensions. https://arxiv.org/abs/math/0302070

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