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

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 . keywords: Ginzburg-Landau functional, OE 6 theory, Moser-Trudinger inequality, Nirenberg problem, phase transition, Chern-Simons Higgs theory 1 Introduction Functionals that exhibit a selfduality phenomenon in the sense that the absolute minimizers satisfy a set of first order partial differential equations are important in various areas of geometry and physics. In the present paper, we investigate a special class of such functionals, namely Ginzburg-Landau type functionals with a 6 th ..

Existence results for mean field equations

Abstract. Let Ω be an annulus. We prove that the mean field equation −∆ψ = ψ = 0 e−βψ Ω e−βψ in Ω on ∂Ω admits a solution for β ∈ (−16π, −8π). This is a supercritical case for the Moser-Trudinger inequality