On moving Ginzburg-Landau filament vortices
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Submission date: 15. Jul. 2002
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
Keywords and phrases: elliptic energy monotonicity, parabolic energy monotonicity, intrinsic hodge decomposition
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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 .