A review of the tangent space in sub-Finsler geometry and applications to the failure of the $\mathsf{CD}$ condition
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910811475148800 |
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| author | Magnabosco, Mattia Rossi, Tommaso |
| author_facet | Magnabosco, Mattia Rossi, Tommaso |
| contents | We review the construction of the tangent space to a sub-Finsler manifold in the measured Gromov-Hausdorff sense. Under suitable assumptions on the measure, the metric measure tangent is described by the nilpotent approximation, equipped with a scalar multiple of the Lebesgue measure. We apply this result in the study of the Lott-Sturm-Villani curvature-dimension condition in sub-Finsler geometry. In particular, we show the failure of the $\mathsf{CD}$ condition in 3D-contact sub-Finsler manifolds, equipped with a bounded measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A review of the tangent space in sub-Finsler geometry and applications to the failure of the $\mathsf{CD}$ condition Magnabosco, Mattia Rossi, Tommaso Differential Geometry Metric Geometry We review the construction of the tangent space to a sub-Finsler manifold in the measured Gromov-Hausdorff sense. Under suitable assumptions on the measure, the metric measure tangent is described by the nilpotent approximation, equipped with a scalar multiple of the Lebesgue measure. We apply this result in the study of the Lott-Sturm-Villani curvature-dimension condition in sub-Finsler geometry. In particular, we show the failure of the $\mathsf{CD}$ condition in 3D-contact sub-Finsler manifolds, equipped with a bounded measure. |
| title | A review of the tangent space in sub-Finsler geometry and applications to the failure of the $\mathsf{CD}$ condition |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2404.16460 |