On sections of complex line bundles over surfaces minimizing a Ginzburg-Landau energy

Abstract

In this work we extend some of the results of Ignat and Jerrard for Ginzburg-Landau vortices of tangent vector fields on two-dimensional Riemannian manifolds to the setting of complex hermitian line bundles. In particular, we elucidate the locations of vortices for the cases of Q-tensors and their higher-rank analogs on a sphere.