Harmonic spinors on axisymmetric 3-manifolds with Melvin ends
arXiv:1407.3529
Abstract
We prove the existence of harmonic spinor fields in axisymmetric Riemannian 3-manifolds having nonnegative scalar curvature and asymptotic to the usual constant time hypersurface of Melvin's magnetic universe. Such a spinor can be used in the proof of the uniqueness of the magnetized Schwarzschild solution.
12 pages. Some details added