Deformations of multivalued harmonic functions
Differential Geometry
2019-12-19 v1
Abstract
We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Nash-Moser implicit function theorem.
Cite
@article{arxiv.1912.08274,
title = {Deformations of multivalued harmonic functions},
author = {Simon Donaldson},
journal= {arXiv preprint arXiv:1912.08274},
year = {2019}
}