Uniqueness of selfdual periodic Chern—Simons vortices of topological-type

Tarantello, Gabriella
June 2007
Calculus of Variations & Partial Differential Equations;Jun2007, Vol. 29 Issue 2, p191
Academic Journal
In analogy with the abelian Maxwell–Higgs model (cf. Jaffe and Taubes in Vortices and monopoles, 1980) we prove that periodic topological-type selfdual vortex-solutions for the Chern–Simons model of Jackiw–Weinberg [Phys Rev Lett 64:2334–2337, 1990] and Hong et al. Phys Rev Lett 64:2230–2233, 1990 are uniquely determined by the location of their vortex points, when the Chern–Simons coupling parameter is sufficiently small. This result follows by a uniqueness and uniform invertibility property established for a related elliptic problem (see Theorem 3.6 and 3.7).


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