Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916746836836352 |
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| author | Speight, Gareth Zimmerman, Scott |
| author_facet | Speight, Gareth Zimmerman, Scott |
| contents | We show that, in arbitrary Carnot groups, pliability in a subset of directions is sufficient to guarantee the existence of a Whitney-type extension and a Lusin approximation for curves with tangent vectors in the same set of directions. We apply this to show that every horizontal curve in the Engel group must intersect a $C^{1}$ horizontal curve in a set of positive measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups Speight, Gareth Zimmerman, Scott Differential Geometry 53C17, 58C25 We show that, in arbitrary Carnot groups, pliability in a subset of directions is sufficient to guarantee the existence of a Whitney-type extension and a Lusin approximation for curves with tangent vectors in the same set of directions. We apply this to show that every horizontal curve in the Engel group must intersect a $C^{1}$ horizontal curve in a set of positive measure. |
| title | Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups |
| topic | Differential Geometry 53C17, 58C25 |
| url | https://arxiv.org/abs/2505.14678 |