Poincaré and Sobolev inequalities for differential forms in Heisenberg groups

Inégalités de Poincaré et de Sobolev pour les formes différentielles sur les groupes de Heisenberg

Annalisa Baldi (1) , Bruno Franchi (1) , Pierre Pansu (2)

1 Dipartimento di Matematica [Bologna]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Poincaré and Sobolev inequalities for differential forms on Heisenberg balls, involving Rumin's differentials, are given. Furthermore, a global homotopy of Rumin's complex which improves differentiability of Rumin forms is provided on any bounded geometry contact manifold.

Mots clés: contact manifolds; homotopy formula.; Sobolev-Poincare inequalities; differential forms; Heisenberg groups

Domaines: Géométrie différentielle [math.DG]; Analyse fonctionnelle [math.FA]

Annalisa Baldi, Bruno Franchi, Pierre Pansu. Poincaré and Sobolev inequalities for differential forms in Heisenberg groups. 2017. ⟨hal-01628688v2⟩