Differential forms in Carnot groups: a G-convergence approach

Baldi, Annalisa; Franchi, Bruno
January 2012
Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p211
Academic Journal
Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex ( E, d) of 'intrinsic' differential forms. In this paper we prove that, in a free Carnot group of step ?, intrinsic 1-forms as well as their intrinsic differentials d appear naturally as limits of usual 'Riemannian' differentials d, e > 0. More precisely, we show that L-energies associated with e d on 1 forms G-converge, as e ? 0, to the energy associated with d.


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