Curvature exponent of sub-Finsler Heisenberg groups
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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_ | 1866915392604078080 |
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| author | Borza, Samuël Magnabosco, Mattia Rossi, Tommaso Tashiro, Kenshiro |
| author_facet | Borza, Samuël Magnabosco, Mattia Rossi, Tommaso Tashiro, Kenshiro |
| contents | The curvature exponent $N_{\mathrm{curv}}$ of a metric measure space is the smallest number $N$ for which the measure contraction property $\mathsf{MCP}(0,N)$ holds. In this paper, we study the curvature exponent of sub-Finsler Heisenberg groups equipped with the Lebesgue measure. We prove that $N_{\mathrm{curv}} \geq 5$, and the equality holds if and only if the corresponding sub-Finsler Heisenberg group is actually sub-Riemannian. Furthermore, we show that for every $N\geq 5$, there is a sub-Finsler structure on the Heisenberg group such that $N_{\mathrm{curv}}=N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature exponent of sub-Finsler Heisenberg groups Borza, Samuël Magnabosco, Mattia Rossi, Tommaso Tashiro, Kenshiro Metric Geometry Differential Geometry 53C17, 53C23, 49J52 The curvature exponent $N_{\mathrm{curv}}$ of a metric measure space is the smallest number $N$ for which the measure contraction property $\mathsf{MCP}(0,N)$ holds. In this paper, we study the curvature exponent of sub-Finsler Heisenberg groups equipped with the Lebesgue measure. We prove that $N_{\mathrm{curv}} \geq 5$, and the equality holds if and only if the corresponding sub-Finsler Heisenberg group is actually sub-Riemannian. Furthermore, we show that for every $N\geq 5$, there is a sub-Finsler structure on the Heisenberg group such that $N_{\mathrm{curv}}=N$. |
| title | Curvature exponent of sub-Finsler Heisenberg groups |
| topic | Metric Geometry Differential Geometry 53C17, 53C23, 49J52 |
| url | https://arxiv.org/abs/2407.14619 |