On the self-dual Einstein-Maxwell-Higgs equation on compact surfaces
On the self-dual Einstein-Maxwell-Higgs equation on compact surfaces
In this paper, we study the self-dual Einstein-Maxwell-Higgs equation on compact surfaces. The solution structure depends on the parameter $\varepsilon $ appearing in the equation. We find an upper bound $\varepsilon _c $ of $\varepsilon $ for the existence of solutions. By using the topological degree theory, we prove that …