On Sections of Complex Line Bundles Over Surfaces Minimizing a Ginzburg–Landau Energy
摘要
In this work, we extend some of the results of Ignat and Jerrard (Arch Ration Mech Anal 239(3):1577–1666, 2021) for Ginzburg–Landau vortices of tangent vector fields on 2-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.