Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex $(E_0^*,d_c)$ of intrinsic'' differential forms. In this paper we prove that, in a free Carnot group of step $\kappa$, intrinsic 1-forms as well as their intrinsic differentials $d_c$ appear naturally as limits of usual Riemannian'' differentials $d_\eps$, $\eps>0$. More precisely, we show that $L^2$-energies associated with $\eps^{-\kappa}d_\eps$ on 1-forms $\Gamma$-converge, as $\eps\to 0$, to the energy associated with $d_c$.

### 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 $(E_0^*,d_c)$ of intrinsic'' differential forms. In this paper we prove that, in a free Carnot group of step $\kappa$, intrinsic 1-forms as well as their intrinsic differentials $d_c$ appear naturally as limits of usual Riemannian'' differentials $d_\eps$, $\eps>0$. More precisely, we show that $L^2$-energies associated with $\eps^{-\kappa}d_\eps$ on 1-forms $\Gamma$-converge, as $\eps\to 0$, to the energy associated with $d_c$.
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A. Baldi; B. Franchi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/110396
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