## 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 , where the word « contact » is meant to stress that de Rham’s exterior differential is replaced by the « exterior differential » of the so-called Rumin’s complex .
A crucial feature of Rumin’s construction is that recovers the scale invariance of the « exterior differential » under the group dilations associated with the stratification of the Lie algebra of . These inequalities provide a natural extension of the corresponding usual inequalities for functions in and are a quantitative formulation of the fact that -closed forms are locally -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
juin 2019 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Sud F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Laboratoire Formation