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

Lin, Fanghua, and Rivière, Tristan. "Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents." Journal of the European Mathematical Society 001.3 (1999): 237-311. <http://eudml.org/doc/277610>.

@article{Lin1999,
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.},
author = {Lin, Fanghua, Rivière, Tristan},
journal = {Journal of the European Mathematical Society},
keywords = {Ginzburg-Landau relaxation; Ginzburg-Landau minimizers; unimodular harmonic map; Ginzburg-Landau minimizer; harmonic map; superconductivity},
language = {eng},
number = {3},
pages = {237-311},
publisher = {European Mathematical Society Publishing House},
title = {Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents},
url = {http://eudml.org/doc/277610},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Lin, Fanghua
AU - Rivière, Tristan
TI - Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 3
SP - 237
EP - 311
AB - 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.
LA - eng
KW - Ginzburg-Landau relaxation; Ginzburg-Landau minimizers; unimodular harmonic map; Ginzburg-Landau minimizer; harmonic map; superconductivity
UR - http://eudml.org/doc/277610
ER -