English

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.

Keywords

Cite

@article{arxiv.1912.08274,
  title  = {Deformations of multivalued harmonic functions},
  author = {Simon Donaldson},
  journal= {arXiv preprint arXiv:1912.08274},
  year   = {2019}
}
R2 v1 2026-06-23T12:49:01.920Z