Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910055906934784 |
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| author | He, Siqi Salm, Willem Adriaan |
| author_facet | He, Siqi Salm, Willem Adriaan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14949 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms He, Siqi Salm, Willem Adriaan Differential Geometry 53C99 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. |
| title | Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms |
| topic | Differential Geometry 53C99 |
| url | https://arxiv.org/abs/2603.14949 |