Preprint 57/2002
On moving Ginzburg-Landau filament vortices
Changyou Wang
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Submission date: 15. Jul. 2002
Pages: 18
published in: Communications in analysis and geometry, 12 (2004) 5, p. 1185-1199 
DOI number (of the published article): 10.4310/CAG.2004.v12.n5.a10
Bibtex
Keywords and phrases: elliptic energy monotonicity, parabolic energy monotonicity, intrinsic hodge decomposition
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Abstract:
In this note, we establish a quantization property
for the heat equation of Ginzburg-Landau functional
in 
which models moving filament vortices.
It asserts that if the energy is sufficiently
small on a parabolic ball in 
then there is no filament vortices in the parabolic
ball of 
radius. This extends a recent
result of Lin-Riviere in 
but the problem
is open for 
for 
.