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 1loc(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. © European Mathematical Society 2010.