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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| Format: | Article |
| Language: | English |
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University of Bologna
2011-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | http://mathematicalanalysis.unibo.it/article/view/2664 |
| _version_ | 1811224716155813888 |
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| author | Annalisa Baldi |
| author_facet | Annalisa Baldi |
| author_sort | Annalisa Baldi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T08:53:58Z |
| format | Article |
| id | doaj.art-64f9d17a72e043819e8b9000ce636d99 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-04-12T08:53:58Z |
| publishDate | 2011-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-64f9d17a72e043819e8b9000ce636d992022-12-22T03:39:29ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292011-12-01212477Differential forms in Carnot groups: a variational approachAnnalisa Baldi0Università di BolognaCarnot 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.http://mathematicalanalysis.unibo.it/article/view/2664Carnot groupsdifferential formsgamma-convergence |
| spellingShingle | Annalisa Baldi Differential forms in Carnot groups: a variational approach Bruno Pini Mathematical Analysis Seminar Carnot groups differential forms gamma-convergence |
| title | Differential forms in Carnot groups: a variational approach |
| title_full | Differential forms in Carnot groups: a variational approach |
| title_fullStr | Differential forms in Carnot groups: a variational approach |
| title_full_unstemmed | Differential forms in Carnot groups: a variational approach |
| title_short | Differential forms in Carnot groups: a variational approach |
| title_sort | differential forms in carnot groups a variational approach |
| topic | Carnot groups differential forms gamma-convergence |
| url | http://mathematicalanalysis.unibo.it/article/view/2664 |
| work_keys_str_mv | AT annalisabaldi differentialformsincarnotgroupsavariationalapproach |