Hypergenerated Carnot groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910899863814144 |
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| author | Donne, Enrico Le Nalon, Luca Paddeu, Nicola Verzellesi, Simone |
| author_facet | Donne, Enrico Le Nalon, Luca Paddeu, Nicola Verzellesi, Simone |
| contents | In this paper we provide an algebraic characterization of those stratified groups in which boundaries with locally constant normal are locally flat. We show that these groups, which we call hypergenerated, are exactly the stratified groups where embeddings of non-characteristic hypersurfaces are locally bi-Lipschitz. Finally, we extend these results to submanifolds of arbitrary codimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypergenerated Carnot groups Donne, Enrico Le Nalon, Luca Paddeu, Nicola Verzellesi, Simone Metric Geometry Differential Geometry Group Theory 22E25, 53C17, 28A33 In this paper we provide an algebraic characterization of those stratified groups in which boundaries with locally constant normal are locally flat. We show that these groups, which we call hypergenerated, are exactly the stratified groups where embeddings of non-characteristic hypersurfaces are locally bi-Lipschitz. Finally, we extend these results to submanifolds of arbitrary codimension. |
| title | Hypergenerated Carnot groups |
| topic | Metric Geometry Differential Geometry Group Theory 22E25, 53C17, 28A33 |
| url | https://arxiv.org/abs/2503.24161 |