Instability of Ginzburg—Landau vortices on manifolds

Abstract

We investigate two settings of the Ginzburg—Landau system posed on a manifold where vortices are unstable. The first is an instability result for critical points with vortices of the Ginzburg—Landau energy posed on a simply connected, compact, closed 2-manifold. The second is a vortex annihilation result for the Ginzburg—Landau heat flow posed on certain surfaces of revolution with boundary.