A note on the diameter of small sub-Riemannian balls
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914387144474624 |
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| author | Di Marco, Marco Somma, Gianluca Vittone, Davide |
| author_facet | Di Marco, Marco Somma, Gianluca Vittone, Davide |
| contents | We observe that the diameter of small (in a locally uniform sense) balls in $C^{1,1}$ sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to $C^0$, the diameter is arbitrarily close to twice the radius. Both results hold independently of the bracket-generating condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the diameter of small sub-Riemannian balls Di Marco, Marco Somma, Gianluca Vittone, Davide Optimization and Control Differential Geometry Metric Geometry 53C17, 28A75 We observe that the diameter of small (in a locally uniform sense) balls in $C^{1,1}$ sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to $C^0$, the diameter is arbitrarily close to twice the radius. Both results hold independently of the bracket-generating condition. |
| title | A note on the diameter of small sub-Riemannian balls |
| topic | Optimization and Control Differential Geometry Metric Geometry 53C17, 28A75 |
| url | https://arxiv.org/abs/2505.02790 |