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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12138 |
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| _version_ | 1866913359458205696 |
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| author | Zimmerman, Scott |
| author_facet | Zimmerman, Scott |
| contents | This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal directions in the Euclidean sense are continuously Pansu differentiable. This proof contains primarily Euclidean arguments and also reproves a version of Magnani's mean value estimate for continuously Pansu differentiable maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the equivalence of derivatives for maps between Carnot groups Zimmerman, Scott Metric Geometry Differential Geometry 30L99 (Primary) 53B40, 35R03 (Secondary) This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal directions in the Euclidean sense are continuously Pansu differentiable. This proof contains primarily Euclidean arguments and also reproves a version of Magnani's mean value estimate for continuously Pansu differentiable maps. |
| title | On the equivalence of derivatives for maps between Carnot groups |
| topic | Metric Geometry Differential Geometry 30L99 (Primary) 53B40, 35R03 (Secondary) |
| url | https://arxiv.org/abs/2405.12138 |