Volume comparison on finite-volume hyperbolic 3-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918135233249280 |
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| author | Jiang, Ruojing Pallete, Franco Vargas |
| author_facet | Jiang, Ruojing Pallete, Franco Vargas |
| contents | On finite-volume hyperbolic $3$-manifolds, we compare volumes of different metrics using the exponential convergence of Ricci-DeTurck flow toward the hyperbolic metric $h_0$. We prove that among metrics with scalar curvature bounded below by $-6$, $h_0$ minimizes the volume. Moreover, for metrics that are either uniformly $C^2$-close to $h_0$ or asymptotically cusped of order at least two, equality holds if and only if the metric is isometric to $h_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volume comparison on finite-volume hyperbolic 3-manifolds Jiang, Ruojing Pallete, Franco Vargas Differential Geometry Geometric Topology On finite-volume hyperbolic $3$-manifolds, we compare volumes of different metrics using the exponential convergence of Ricci-DeTurck flow toward the hyperbolic metric $h_0$. We prove that among metrics with scalar curvature bounded below by $-6$, $h_0$ minimizes the volume. Moreover, for metrics that are either uniformly $C^2$-close to $h_0$ or asymptotically cusped of order at least two, equality holds if and only if the metric is isometric to $h_0$. |
| title | Volume comparison on finite-volume hyperbolic 3-manifolds |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2509.03566 |