Wang, Changyou On moving Ginzburg-Landau vortices. (English) Zbl 1063.35081 Commun. Anal. Geom. 12, No. 5, 1185-1199 (2004). Summary: We establish a quantization property for the heat equation of Ginzburg-Landau functional in \(\mathbb{R}^4\) which models moving vortices of surface types. It asserts that if the energy is sufficiently small on a parabolic ball in \(\mathbb{R}^4\times\mathbb{R}_+\), then there is no vortice in the parabolic ball of \(\frac 12\) radius. This extends a recent result of F.-H. Lin and T. Rivière [Commun. Pure Appl. Math. 54, No. 7, 826–850 (2001; Zbl 1029.35127)] in \(\mathbb{R}^3\). Cited in 7 Documents MSC: 35K55 Nonlinear parabolic equations 35K15 Initial value problems for second-order parabolic equations 35B45 A priori estimates in context of PDEs Keywords:quantization property Citations:Zbl 1029.35129; Zbl 1029.35127 PDFBibTeX XMLCite \textit{C. Wang}, Commun. Anal. Geom. 12, No. 5, 1185--1199 (2004; Zbl 1063.35081) Full Text: DOI