| Abstract: |
| In this talk, we consider the self-dual equations arising from the Maxwell-Chern-Simons-Higgs model on $\mathbb{R}^{1,2}$ equipped with a background metric $(1,-b(x),-b(x))$. We assume that $b(x)$ is not a constant and satisfies $b(x)=O(|x|^{-\ga})$ at infinity with $\ga \in (0,2)$. The main equations have two important parameters: the Maxwell coupling constant $\kappa$ and the Chern-Simons coupling constant $q$. We show that there exists a constant $\beta_*>0$ such that there exists a topological solution provided $\kappa q >\beta_*$. We also verify the Chern-Simons limit for those solutions. |
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