Nonsimple closed geodesics with given intersection number on hyperbolic surfaces
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915422209572864 |
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| author | Shen, Wujie |
| author_facet | Shen, Wujie |
| contents | We prove that the minimal length of a closed geodesic with self-intersection number $k$ on any finite-type hyperbolic surface is $2\cosh^{-1}(1+2k)$ for $k>1750$. This improves the previously known threshold $k > 10^{13350}$. Our proof is independent of it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonsimple closed geodesics with given intersection number on hyperbolic surfaces Shen, Wujie Geometric Topology We prove that the minimal length of a closed geodesic with self-intersection number $k$ on any finite-type hyperbolic surface is $2\cosh^{-1}(1+2k)$ for $k>1750$. This improves the previously known threshold $k > 10^{13350}$. Our proof is independent of it. |
| title | Nonsimple closed geodesics with given intersection number on hyperbolic surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2305.00638 |