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MiS Preprint

On moving Ginzburg-Landau filament vortices

Changyou Wang


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 $n\ge 5$.

elliptic energy monotonicity, parabolic energy monotonicity, intrinsic hodge decomposition

Related publications

2004 Repository Open Access
Chaofeng Wang

On moving Ginzburg-Landau filament vortices

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