Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms
Differential Geometry
2026-03-18 v2
Abstract
We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to a nearby non-degenerate Z/2-harmonic 1-form. Our argument combines analysis of the leading coefficients in the local expansion under metric perturbations with a quantitative Nash-Moser implicit function theorem.
Keywords
Cite
@article{arxiv.2603.14949,
title = {Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms},
author = {Siqi He and Willem Adriaan Salm},
journal= {arXiv preprint arXiv:2603.14949},
year = {2026}
}
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