Revista Matemática Iberoamericana


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Volume 35, Issue 3, 2019, pp. 643–692
DOI: 10.4171/rmi/1065

Published online: 2019-04-01

Gaffney–Friedrichs inequality for differential forms on Heisenberg groups

Bruno Franchi[1], Francescopaolo Montefalcone[2] and Elena Serra[3]

(1) Università di Bologna, Italy
(2) Università degli Studi di Padova, Italy
(3) Università di Bologna, Italy

In this paper, we will prove several generalized versions, dependent on different boundary conditions, of the classical Gaffney–Friedrichs inequality for differential forms on Heisenberg groups. In the first part of the paper, we will consider horizontal differential forms and the horizontal differential. In the second part, we shall prove the counterpart of these results in the context of Rumin’s complex.

Keywords: Heisenberg groups, horizontal differential forms, Rumin’s complex, Gaffney–Friedrichs inequalities

Franchi Bruno, Montefalcone Francescopaolo, Serra Elena: Gaffney–Friedrichs inequality for differential forms on Heisenberg groups. Rev. Mat. Iberoam. 35 (2019), 643-692. doi: 10.4171/rmi/1065