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Explicit elliptic estimates for nowhere vanishing harmonic 1-forms (2512.21751v1)
Published 25 Dec 2025 in math.DG
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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