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Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere. (English) Zbl 0913.53032
Summary: We consider a Ginzburg-Landau type functional on $$S^2$$ with a 6-th 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 $$S^2$$.

##### MSC:
 53Z05 Applications of differential geometry to physics 81T13 Yang-Mills and other gauge theories in quantum field theory 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 58Z05 Applications of global analysis to the sciences 82B26 Phase transitions (general) in equilibrium statistical mechanics
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