Differential forms in Carnot groups: a variational approach

Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex of ``intrinsic'' differential forms. In this paper we want to provide an evidence of the intrinsic character of Rumin's complex, in the spirit of the Riemannian approximation, like...

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Bibliographic Details
Main Author: Annalisa Baldi
Format: Article
Language:English
Published: University of Bologna 2011-12-01
Series:Bruno Pini Mathematical Analysis Seminar
Subjects:
Online Access:http://mathematicalanalysis.unibo.it/article/view/2664
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Summary:Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex of ``intrinsic'' differential forms. In this paper we want to provide an evidence of the intrinsic character of Rumin's complex, in the spirit of the Riemannian approximation, like in e.g., the notes of Gromov (Textes Mathématiques 1981) and in Rumin (Geom. Funct. Anal.,2000) . More precisely, we want to show that the intrinsic differential is a limit of suitably weighted usual first order de Rham differentials. As an application, we prove that the L^2-energies associated to classical Maxwell's equations in R^n Gamma-converges to the L^2-energies associated to an ''intrinsic'' Maxwell's equation in a free Carnot group.
ISSN:2240-2829