Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7

Abstract

For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global minimizer uε of this problem; moreover, uε is symmetric and of the form uε(x)=fε(|x|)x|x| for x∈BN.