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 $\mathbbH^n$, 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 $\mathbbH^n$. These inequalities provide a natural extension of the corresponding usual inequalities for functions in $\mathbbH^n$ 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