Explicit elliptic estimates for nowhere vanishing harmonic 1-forms
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911339216109568 |
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| author | Deep, Arham |
| author_facet | Deep, Arham |
| contents | We compute an explicit constant for an injectivity estimate on the 3-Torus involving the Laplace Operator. First, we provide motivation for such explicit estimates. We perform the computation for the 3-Torus endowed with the flat metric before generalising to perturbed metrics. Finally, we apply these results to show existence of a nowhere vanishing harmonic 1-form on the 3-Torus endowed with a perturbed metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit elliptic estimates for nowhere vanishing harmonic 1-forms Deep, Arham Differential Geometry We compute an explicit constant for an injectivity estimate on the 3-Torus involving the Laplace Operator. First, we provide motivation for such explicit estimates. We perform the computation for the 3-Torus endowed with the flat metric before generalising to perturbed metrics. Finally, we apply these results to show existence of a nowhere vanishing harmonic 1-form on the 3-Torus endowed with a perturbed metric. |
| title | Explicit elliptic estimates for nowhere vanishing harmonic 1-forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.21751 |