On the bifurcation theory of the Ginzburg-Landau equations

Abstract

We construct nonminimal and irreducible solutions to the Ginzburg-Landau equations on closed manifolds of arbitrary dimension with trivial first real cohomology. Our method uses bifurcation theory where the "bifurcation points" are characterized by the eigenvalues of a Laplace-type operator. To our knowledge these are the first such examples on nontrivial line bundles.

15 pages, no figures, accepted version, comments are welcome! To appear in the Proceedings of the AMS. arXiv admin note: text overlap with arXiv:2103.05613

References in corpus (1)

• Convergence of the self-dual $U(1)$-Yang-Mills-Higgs energies to the $(n-2)$-area functional