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.
An introduction to the study of critical points of solutions of elliptic and parabolic equations
A construction of patterns with many critical points on topological tori
Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains
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