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

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

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