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arXiv · 2203.13701

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

Annalisa Baldi·Maria Carla Tesi·Francesca Tripaldi
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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.

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Annalisa Baldi, Maria Carla Tesi, Francesca Tripaldi. 2022-03-25. Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry. https://doi.org/10.1515/ans-2022-0022

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