Deformations of multivalued harmonic functions

Published 17 Dec 2019 in math.DG | (1912.08274v1)

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

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