Accepted Paper
Inserted: 2 jan 2023
Last Updated: 2 jan 2023
Journal: Advanced Nonlinear Studies
Volume: 22
Number: 1
Pages: 484-516
Year: 2022
Doi: https://doi.org/10.1515/ans-2022-0022
Abstract:
In this article, we establish a Gaffney type inequality, in $W^{\ell,p}$ -Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds). Here, $p\in]1,\infty[$ and $\ell=1,2$ depending on the order of the differential form we are considering. The proof relies on the structure of the Rumin’s complex of differential forms in contact manifolds, on a Sobolev-Gaffney inequality proved by Baldi-Franchi in the setting of the Heisenberg groups and on some geometric properties that can be proved for sub-Riemannian contact manifolds with bounded geometry.