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Adriano Pisante

2011-01-10
10:30:00 - 10:55:00

R102 , Astronomy and Mathematics Building

We discuss new symmetry results for nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in ${H}^{1}_{\rm{loc}}(\mathbb{R}^3;\mathbb{R}^3)$ satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit map equivariant under the action of the orthogonal group. More generally, for any $N\geq 3$ we characterize the $O(N)-$equivariant vortex solution for Ginzburg-Landau type equations in the $N-$dimensional Euclidean space and we prove its local energy minimality for the corresponding energy functional.

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