Maxwell-Chern-Simons vortices on compact surfaces: Nonequivalence of the first and the second order equations

摘要

In this paper we study the Maxwell-Chern-Simons-Higgs and the Chern-Simons-Higgs vortices on a compact Riemann surface. We establish the existence of a solution of the static Maxwell-Chern-Simons-Higgs vortex equations, which is a minimizer of the static energy functional. This shows the nonequivalence of the first and the second order Maxwell-Chern-Simons-Higgs vortex equations. The nonequivalence is also proved for the Chern-Simons-Higgs vortices by verifying the Chern-Simons limit.