Carnot rectifiability and Alberti representations
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Wiley Open Access
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| Format: | Artículo Open Access |
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Wiley
2025
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| _version_ | 1867010186272571392 |
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| author | G. Antonelli E. Le Donne A. Merlo |
| author_facet | G. Antonelli E. Le Donne A. Merlo G. Antonelli E. Le Donne A. Merlo |
| collection | Wiley Open Access |
| contents | Carnot rectifiability and Alberti representations G. Antonelli E. Le Donne A. Merlo Proceedings of the London Mathematical Society AbstractA metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability of Lipschitz maps with values in Carnot groups. In order to obtain this characterisation, we develop and study the analogue of the notion of Lipschitz differentiability space by Cheeger, using Carnot groups and Pansu derivatives as models. We call such metric measure spaces Pansu differentiability spaces. 10.1112/plms.70021 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1112/plms.70021 |
| format | Artículo Open Access |
| id | wiley_oa_10_1112_plms_70021 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2025 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Carnot rectifiability and Alberti representations G. Antonelli E. Le Donne A. Merlo Proceedings of the London Mathematical Society Carnot rectifiability and Alberti representations G. Antonelli E. Le Donne A. Merlo Proceedings of the London Mathematical Society AbstractA metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability of Lipschitz maps with values in Carnot groups. In order to obtain this characterisation, we develop and study the analogue of the notion of Lipschitz differentiability space by Cheeger, using Carnot groups and Pansu derivatives as models. We call such metric measure spaces Pansu differentiability spaces. 10.1112/plms.70021 http://creativecommons.org/licenses/by/4.0/ |
| title | Carnot rectifiability and Alberti representations |
| topic | Proceedings of the London Mathematical Society |
| url | https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.70021 |