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

Weiyue Ding, Jürgen Jost, Jiayu Li, and Guofang Wang

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Submission date: 03. Jul. 1998
Pages: 27
published in: Commentarii mathematici Helvetici, 74 (1999) 1, p. 118-142 
DOI number (of the published article): 10.1007/s000140050079
Bibtex
Keywords and phrases: ginzburg-landau functional, moser-trudinger inequality, nirenberg problem, phase transition, chern-simons higgs theory
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Abstract:
We consider a Ginzburg-Landau type functional on S² 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 S².