The Parabolic $U(1)$-Higgs Equations and Codimension-two Mean Curvature Flows

Davide Parise, Alessandro Pigati, Daniel Stern

We develop the asymptotic analysis as $\epsilon \to 0$ for the natural gradient flow of the self-dual $U(1)$-Higgs energies $$E_ε(u,\nabla)=\int_M\left(|\nabla u|^2+ε^2|F_{\nabla}|^2+\frac…