THE SELF-DUAL CHERN–SIMONS HIGGS EQUATION ON A COMPACT RIEMANN SURFACE WITH BOUNDARY

We study the self-dual Chern–Simons Higgs equation on a compact Riemann surface with Neumann boundary condition. We show that the Chern–Simons Higgs equation with parameter λ > 0 has at least two solutions [Formula: see text] for λ sufficiently large, such that [Formula: see text] almost everywhere as λ → + ∞, and that [Formula: see text] almost everywhere as λ → ∞, where u0 is a (negative) Green function on M.