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arXiv · 2512.21751

Explicit elliptic estimates for nowhere vanishing harmonic 1-forms

Arham Deep
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Abstract

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.

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Arham Deep. 2025-12-25. Explicit elliptic estimates for nowhere vanishing harmonic 1-forms. https://arxiv.org/abs/2512.21751

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