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Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1-valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology class induced from the S 1-valued boundary data. The union of this harmonic map and the minimal current is the natural generalization of the harmonic extension. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970050008
Publisher site
See Article on Publisher Site

Abstract

There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1-valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology class induced from the S 1-valued boundary data. The union of this harmonic map and the minimal current is the natural generalization of the harmonic extension.

Journal

Journal of the European Mathematical Society – Springer Journals

Published: Sep 1, 1999

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