Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911105864957952 |
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| author | Cremaschi, Tommaso Giovannini, Viola Schlenker, Jean-Marc |
| author_facet | Cremaschi, Tommaso Giovannini, Viola Schlenker, Jean-Marc |
| contents | We provide conditions under which a Riemann surface $X$ is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on $X$ enough closed curves of short enough hyperbolic length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume Cremaschi, Tommaso Giovannini, Viola Schlenker, Jean-Marc Differential Geometry High Energy Physics - Theory Geometric Topology 57K32 We provide conditions under which a Riemann surface $X$ is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on $X$ enough closed curves of short enough hyperbolic length. |
| title | Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume |
| topic | Differential Geometry High Energy Physics - Theory Geometric Topology 57K32 |
| url | https://arxiv.org/abs/2405.07598 |