New properties of length-extremals in free step-2 rank-4 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_ | 1866909999387639808 |
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| author | Montanari, Annamaria Morbidelli, Daniele |
| author_facet | Montanari, Annamaria Morbidelli, Daniele |
| contents | In the free, step-2, rank-4 sub-Riemannian Carnot group, we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut-locus of the origin. Finally, we give some upper estimates for the cut-time of extremals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New properties of length-extremals in free step-2 rank-4 Carnot groups Montanari, Annamaria Morbidelli, Daniele Metric Geometry Classical Analysis and ODEs In the free, step-2, rank-4 sub-Riemannian Carnot group, we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut-locus of the origin. Finally, we give some upper estimates for the cut-time of extremals. |
| title | New properties of length-extremals in free step-2 rank-4 Carnot groups |
| topic | Metric Geometry Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.00021 |