On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912559839313920 |
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| author | Jiang, Ruojing Pallete, Franco Vargas |
| author_facet | Jiang, Ruojing Pallete, Franco Vargas |
| contents | On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a weighted Hölder norm. A key ingredient of our approach is the application of interpolation theory.
Furthermore, this result is a valuable tool for investigating minimal surface entropy, which quantifies the growth rate of the number of closed minimal surfaces in terms of genus. We explore this in [17]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume Jiang, Ruojing Pallete, Franco Vargas Differential Geometry Analysis of PDEs 53E20 On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a weighted Hölder norm. A key ingredient of our approach is the application of interpolation theory. Furthermore, this result is a valuable tool for investigating minimal surface entropy, which quantifies the growth rate of the number of closed minimal surfaces in terms of genus. We explore this in [17]. |
| title | On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume |
| topic | Differential Geometry Analysis of PDEs 53E20 |
| url | https://arxiv.org/abs/2509.00188 |