Curvature-dimension condition of sub-Riemannian $α$-Grushin half-spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915447032512512 |
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| author | Borza, Samuël Tashiro, Kenshiro |
| author_facet | Borza, Samuël Tashiro, Kenshiro |
| contents | We provide new examples of sub-Riemannian manifolds with boundary equipped with a smooth measure that satisfy the $\mathsf{RCD}(K , N)$ condition. They are constructed by equipping the half-plane, the hemisphere and the hyperbolic half-plane with a two-dimensional almost-Riemannian structure and a measure that vanishes on their boundary. The construction of these spaces is inspired from the geometry of the $α$-Grushin plane. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_11177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature-dimension condition of sub-Riemannian $α$-Grushin half-spaces Borza, Samuël Tashiro, Kenshiro Metric Geometry Differential Geometry 53C17, 53C21, 49Q22 We provide new examples of sub-Riemannian manifolds with boundary equipped with a smooth measure that satisfy the $\mathsf{RCD}(K , N)$ condition. They are constructed by equipping the half-plane, the hemisphere and the hyperbolic half-plane with a two-dimensional almost-Riemannian structure and a measure that vanishes on their boundary. The construction of these spaces is inspired from the geometry of the $α$-Grushin plane. |
| title | Curvature-dimension condition of sub-Riemannian $α$-Grushin half-spaces |
| topic | Metric Geometry Differential Geometry 53C17, 53C21, 49Q22 |
| url | https://arxiv.org/abs/2409.11177 |