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 . 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}
}