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Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere
Weiyue Ding, Jürgen Jost, Jiayu Li and Guofang Wang
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.