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

2010; European Mathematical Society; Volume: 12; Issue: 5 Linguagem: Inglês

10.4171/jems/223

1435-9863

Vincent Millot, Adriano Pisante,

Advanced Differential Geometry Research

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.