Deformations of multivalued harmonic functions
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Published version
Author(s)
Donaldson, Simon
Type
Journal Article
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.
Date Issued
2021-06-01
Date Acceptance
2021-05-04
Citation
Quarterly Journal of Mathematics, 2021, 72 (1-2), pp.199-235
ISSN
0033-5606
Publisher
Oxford University Press
Start Page
199
End Page
235
Journal / Book Title
Quarterly Journal of Mathematics
Volume
72
Issue
1-2
Copyright Statement
© The Author(s) 2021. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
http://arxiv.org/abs/1912.08274v1
Subjects
ELLIPTIC THEORY
Mathematics
Physical Sciences
Science & Technology
THEOREM
Publication Status
Published
Date Publish Online
2021-03-31