Poincaré inequalities for differential forms on Heisenberg group

Poincaré inequalities
Heisenberg group
Grenoble
[MATH]Mathematics [math]
sub-riemannian
sous-riemannien
sub-riemannian days 2017
journées sous-riemanniennes 2017
differential forms

Appears in collection : Journée sous-riemannienne 2017

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.