Energy Concentration for Min-Max Solutions of the Ginzburg-Landau Equations on Manifolds with $b_1(M)\ne 0$

Daniel Stern

We establish a new estimate for the Ginzburg-Landau energies $E_{\epsilon }(u)={\int }_M\frac{1}{2}|du{|}^2+\frac{1}{4{\epsilon }^2}(1-|u{|}^2{)}^2$ of complex-valued maps $u$ on a compact, oriented manifold $…