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^1_{\mathrm{loc}} (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.