Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry

In this article, we establish a Gaffney type inequality, in We(l,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 is an element of ]1, infinity[ and l = 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.