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

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.