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arXiv · 1912.08274

Deformations of multivalued harmonic functions

Simon Donaldson
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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.

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Simon Donaldson. 2019-12-17. Deformations of multivalued harmonic functions. https://arxiv.org/abs/1912.08274

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