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MiS Preprint
57/2002
On moving Ginzburg-Landau filament vortices
Changyou Wang
Abstract
In this note, we establish a quantization property for the heat equation of Ginzburg-Landau functional in $R^4$ which models moving filament vortices. It asserts that if the energy is sufficiently small on a parabolic ball in $R^4\times R_+$ then there is no filament vortices in the parabolic ball of ${1\over 2}$ radius. This extends a recent result of Lin-Riviere in $R^3$ but the problem is open for $R^n$ for $n\ge 5$.
