Publications
2002
Issue 57

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 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 $\frac{1}{2}$ radius. This extends a recent result of Lin-Riviere in $R^{3}$ but the problem is open for $R^{n}$ for $n \geq 5$ .

Contact the author per mail Download full preprint 165 KB

Received:: 15.07.02

Published:: 15.07.02

Keywords:: elliptic energy monotonicity, parabolic energy monotonicity, intrinsic hodge decomposition

Related publications

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

BibTex DOI: 10.4310/CAG.2004.v12.n5.a10