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arXiv:1912.08274math.DG

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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Subjects
math.DGDifferential Geometry

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  1. Functions are vectors 1 comment

    • > You will not find this in the literature. It would have cost you nothing except a minute or so of your time to have refuted yourself before posting: https://arxiv.org/abs/1912.08274 https://arxiv.org/abs/1703.01700 (See also: https://en.wikipedia.org/wiki/Multivalued_function)

      bigbillheckView on HNParent context

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