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arXiv · 2603.14949

Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms

Siqi He·Willem Adriaan Salm
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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.

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Siqi He, Willem Adriaan Salm. 2026-03-16. Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms. https://arxiv.org/abs/2603.14949

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