Frauenfelder, Urs Vortices on the cylinder. (English) Zbl 1119.58010 Int. Math. Res. Not. 2006, No. 14, Article ID 63130, 34 p. (2006). The author studies the vortex equations which describe the absolute minima of the Yang-Mills-Higgs functional. Given a Riemann surface \(\Sigma\) with a unitary line bundle \(L\), this functional is defined on the space formed by all unitary connections on \(L\) and smooth sections of \(L\). By using the finite-dimensional approximation technique of Furuta, Kronheimer, and Manolescu, the author reproves the result of Jaffe and Taubes that for a given vortex number \(N\) the moduli space of the solutions to the vortex equations on the cylinder \(Z\) modulo gauge equivalence is the \(N\)-fold symmetric power of \(Z\). Reviewer: Iskander A. Taimanov (Novosibirsk) Cited in 4 Documents MSC: 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals Keywords:vortex equations; moduli spaces; Riemann surfaces; Yang-Mills-Higgs functional PDFBibTeX XMLCite \textit{U. Frauenfelder}, Int. Math. Res. Not. 2006, No. 14, Article ID 63130, 34 p. (2006; Zbl 1119.58010) Full Text: DOI arXiv