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