Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Deep, Arham
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117606236
Cites:
Cited by:
Related to: