Instability of Ginzburg-Landau Vortices on Manifolds

Abstract

We investigate two settings of Ginzburg-Landau 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.

Cited by in corpus (3)

• Dynamics Of Ginzburg-Landau And Gross-Pitaevskii Vortices On Manifolds
• Ginzburg-Landau patterns in circular and spherical geometries: vortices, spirals and attractors
• The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution