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 $H_{\mathrm{loc}}^1(R^3;R^3)$ 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.