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

Abstract

In this paper 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 non-compact 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.

36 pages

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