Differential forms in Carnot groups: a Γ-convergence approach

Abstract

Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex (E0*, dc) of “intrinsic” differential forms. In this paper we prove that, in a free Carnot group of step κ, intrinsic 1-forms as well as their intrinsic differentials dc appear naturally as limits of usual “Riemannian” differentials de, e > 0. More precisely, we show that L2-energies associated with e−κde on 1 forms Γ-converge, as e → 0, to the energy associated with dc.