Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908639053217792 |
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| author | Butt, Karen Erchenko, Alena Humbert, Tristan |
| author_facet | Butt, Karen Erchenko, Alena Humbert, Tristan |
| contents | In 2004, Manning showed that the topological entropy of the geodesic flow of a closed surface of non-constant negative curvature is strictly decreasing along the normalized Ricci flow, and he asked if an analogous result holds in higher dimensions for metrics in a neighborhood of a hyperbolic metric. In this paper, we affirmatively answer this question. Namely, we show that the topological entropy of the geodesic flow of a closed Riemannian manifold that carries a hyperbolic metric is indeed strictly decreasing along the normalized Ricci flow starting from a metric of variable negative sectional curvature sufficiently close to the hyperbolic metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric Butt, Karen Erchenko, Alena Humbert, Tristan Differential Geometry Dynamical Systems 53E20, 37D40, 37B40 In 2004, Manning showed that the topological entropy of the geodesic flow of a closed surface of non-constant negative curvature is strictly decreasing along the normalized Ricci flow, and he asked if an analogous result holds in higher dimensions for metrics in a neighborhood of a hyperbolic metric. In this paper, we affirmatively answer this question. Namely, we show that the topological entropy of the geodesic flow of a closed Riemannian manifold that carries a hyperbolic metric is indeed strictly decreasing along the normalized Ricci flow starting from a metric of variable negative sectional curvature sufficiently close to the hyperbolic metric. |
| title | Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric |
| topic | Differential Geometry Dynamical Systems 53E20, 37D40, 37B40 |
| url | https://arxiv.org/abs/2511.06137 |