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Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere

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Commentarii Mathematici Helvetici

Abstract.

We consider a Ginzburg-Landau type functional on S2 with a 6th order potential and the corresponding selfduality equations. We study the limiting behavior in the two vortex case when a coupling parameter tends to zero. This two vortex case is a limiting case for the Moser inequality, and we correspondingly detect a rich and varied asymptotic behavior depending on the position of the vortices. We exploit analogies with the Nirenberg problem for the prescribed Gauss curvature equation on S2.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Bei**g 100080, P. R. China, China

    W. Ding, J. Li & G. Wang

  2. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, Germany, Germany

    J. Jost

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  1. W. Ding
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  2. J. Li
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  3. G. Wang
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  4. J. Jost
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Received: December 3, 1997

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Ding, W., Li, J., Wang, G. et al. Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere. Comment. Math. Helv. 74, 118–142 (1999). https://doi.org/10.1007/s000140050079

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  • DOI: https://doi.org/10.1007/s000140050079

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