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Dispersive and subelliptic PDEs

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

speaker: Bruno Franchi (Università di Bologna)

abstract: In this talk we prove contact Poincar\'e 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 $(E₀^\bullet,d_c)$. A crucial feature of Rumin’s construction is that the ``exterior differential’’ $d_c$ recovers the scale invariance of 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.

timetable:
Tue 11 Feb, 9:20 - 10:10, Aula Dini
documents:

Talk

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