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Differential forms in Carnot groups: a Γ-convergence approach

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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 κ, intrinsic 1-forms as well as their intrinsic differentials d c appear naturally as limits of usual “Riemannian” differentials d ε , ε > 0. More precisely, we show that L 2-energies associated with ε −κ d ε on 1 forms Γ-converge, as ε → 0, to the energy associated with d c .

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Authors and Affiliations

  1. Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Annalisa Baldi & Bruno Franchi

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  1. Annalisa Baldi
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  2. Bruno Franchi
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Correspondence to Bruno Franchi.

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Communicated by L. Ambrosio.

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Baldi, A., Franchi, B. Differential forms in Carnot groups: a Γ-convergence approach. Calc. Var. 43, 211–229 (2012). https://doi.org/10.1007/s00526-011-0409-8

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