On solutions to the Ginzburg-Landau equations in higher dimensions
Simon Brendle
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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