English

On solutions to the Ginzburg-Landau equations in higher dimensions

Differential Geometry 2007-05-23 v2 Analysis of PDEs

Abstract

We establish a glueing theorem for the Ginzburg-Landau equations in dimension n>2n > 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.

Cite

@article{arxiv.math/0302070,
  title  = {On solutions to the Ginzburg-Landau equations in higher dimensions},
  author = {Simon Brendle},
  journal= {arXiv preprint arXiv:math/0302070},
  year   = {2007}
}