P. Pansu - Poincaré inequalities for differential forms on Heisenberg group

Pierre Pansu (1) , Fanny Bastien (2)

1 Département de Mathématiques [ORSAY]
2 IF - Institut Fourier

Every closed differential form ω on a Euclidean ball has a primitive whose Lq norm is bounded by the Lp norm of ω (for suitable exponents p and q). We prove an analogous result for Rumin’s exterior differential on Heisenberg balls. This is used to prove vanishing of `q,p-cohomology of Heisenberg groups. Joint work with Annalisa Baldi and Bruno Franchi.

Mots clés: sub-riemannian days 2017; sub-riemannian; Poincaré inequalities; differential forms; Heisenberg group

Mots clés: journées sous-riemanniennes 2017; sous-riemannien; grenoble

Domaines: Mathématiques [math]

Pierre Pansu, Fanny Bastien. P. Pansu - Poincaré inequalities for differential forms on Heisenberg group: Sub-riemannian days 2017 . 2017. ⟨medihal-01721738⟩