Symmetry results for the area formula in homogeneous groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916410927611904 |
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| author | Corni, Francesca Magnani, Valentino |
| author_facet | Corni, Francesca Magnani, Valentino |
| contents | We prove that if the shape of the metric unit ball in a homogeneous group enjoys a precise symmetry property, then the associated distance yields the standard form of the area formula. The result applies to some classes of smooth and nonsmooth submanifolds. We finally prove the equality between spherical measure and centered Hausdorff measure, under two different geometric conditions on the shape of the metric unit ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry results for the area formula in homogeneous groups Corni, Francesca Magnani, Valentino Metric Geometry We prove that if the shape of the metric unit ball in a homogeneous group enjoys a precise symmetry property, then the associated distance yields the standard form of the area formula. The result applies to some classes of smooth and nonsmooth submanifolds. We finally prove the equality between spherical measure and centered Hausdorff measure, under two different geometric conditions on the shape of the metric unit ball. |
| title | Symmetry results for the area formula in homogeneous groups |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2409.16918 |