A Natural Min-Max Construction for Ginzburg-Landau Functionals

Daniel Stern

We use min-max techniques to produce nontrivial solutions $u_{\epsilon }:M\to {\mathbb{R}}^2$ of the Ginzburg-Landau equation $\Delta u_{\epsilon }+\frac{1}{{\epsilon }^2}(1-|u_{\epsilon }{|}^2)u_{\epsilon }=0$ on a given compact Riemannian…