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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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 $n\ge 5$.

Received:
Jul 15, 2002
Published:
Jul 15, 2002
Keywords:
elliptic energy monotonicity, parabolic energy monotonicity, intrinsic hodge decomposition

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inJournal
2004 Repository Open Access
Chaofeng Wang

On moving Ginzburg-Landau filament vortices

In: Communications in analysis and geometry, 12 (2004) 5, pp. 1185-1199