Symmetry of local minimizers for the three dimensional Ginzburg-Landau functional

Abstract

We classify nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in $H_{loc}^1(R^3;R^3)$ satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit solution equivariant under the action of the orthogonal group.

21 pages