Measured foliations at infinity of quasi-Fuchsian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910930171854848 |
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| author | Marković, Diptaishik Choudhury Vladimir |
| author_facet | Marković, Diptaishik Choudhury Vladimir |
| contents | Let $(λ^+(M),λ^-(M))$ denote the pair of measured foliations at the boundary at infinity $\partial_\infty$ of a quasi-Fuchsian manifold $M$. We prove that $(λ^+(M),λ^-(M))$ is filling if $M$ is close to being Fuchsian. We also show that given any filling pair $(α_1,α_2)$ of measured foliations, and every small enough $t>0$, the pair $(tα_1,tα_2)$ is realised as the pair of measured foliations at infinity of some quasi-Fuchsian manifold $M$. This answers questions of Schlenker near the Fuchsian locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measured foliations at infinity of quasi-Fuchsian manifolds Marković, Diptaishik Choudhury Vladimir Geometric Topology Differential Geometry Let $(λ^+(M),λ^-(M))$ denote the pair of measured foliations at the boundary at infinity $\partial_\infty$ of a quasi-Fuchsian manifold $M$. We prove that $(λ^+(M),λ^-(M))$ is filling if $M$ is close to being Fuchsian. We also show that given any filling pair $(α_1,α_2)$ of measured foliations, and every small enough $t>0$, the pair $(tα_1,tα_2)$ is realised as the pair of measured foliations at infinity of some quasi-Fuchsian manifold $M$. This answers questions of Schlenker near the Fuchsian locus. |
| title | Measured foliations at infinity of quasi-Fuchsian manifolds |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2505.04111 |