Poincaré and Sobolev inequalities for differential forms in Euclidean spaces and Heisenberg groups (in collaboration with A. Baldi & P. Pansu)

Lundi 13 mai 14:00-15:00 - Bruno Franchi - Dipartimento di Matematica, Università di Bologna

Résumé : In this talk we present endpoint Poincaré and Sobolev inequalities for the de Rham complex in Euclidean spaces as well as endpoint contact Poincaré and Sobolev inequalities in Heisenberg groups \mathbb{H}^n, where the word « contact » is meant to stress that de Rham’s exterior differential is replaced by the « exterior differential » d_c of the so-called Rumin’s complex (E_0^\bullet, d_c).
A crucial feature of Rumin’s construction is that d_c recovers the scale invariance of the « exterior differential » d_c under the group dilations associated with the stratification of the Lie algebra of \mathbb{H}^n. These inequalities provide a natural extension of the corresponding usual inequalities for functions in \mathbb{H}^n and are a quantitative formulation of the fact that d_c-closed forms are locally d_c-exact.

Lieu : IMO ; salle 3L8.

Poincaré and Sobolev inequalities for differential forms in Euclidean spaces and Heisenberg groups (in collaboration with A. Baldi & P. Pansu)  Version PDF