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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.14067 |
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| _version_ | 1866913904749182976 |
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| author | Kim, Dongryul M. Lee, Minju |
| author_facet | Kim, Dongryul M. Lee, Minju |
| contents | Let M be a geometrically finite hyperbolic 3-manifold whose limit set is a round Sierpiński gasket, i.e. M is geometrically finite and acylindrical with a compact, totally geodesic convex core boundary. In this paper, we classify orbit closures of the 1-dimensional horocycle flow on the frame bundle of M. As a result, the closure of a horocycle in M is a properly immersed submanifold. This extends the work of McMullen-Mohammadi-Oh where M is further assumed to be convex cocompact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Horocycles in hyperbolic 3-manifolds with round Sierpiński limit sets Kim, Dongryul M. Lee, Minju Dynamical Systems Differential Geometry Geometric Topology Let M be a geometrically finite hyperbolic 3-manifold whose limit set is a round Sierpiński gasket, i.e. M is geometrically finite and acylindrical with a compact, totally geodesic convex core boundary. In this paper, we classify orbit closures of the 1-dimensional horocycle flow on the frame bundle of M. As a result, the closure of a horocycle in M is a properly immersed submanifold. This extends the work of McMullen-Mohammadi-Oh where M is further assumed to be convex cocompact. |
| title | Horocycles in hyperbolic 3-manifolds with round Sierpiński limit sets |
| topic | Dynamical Systems Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2501.14067 |