Short Simple Geodesic Loops on a 2-Sphere
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917074298732544 |
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| author | Beach, Isabel |
| author_facet | Beach, Isabel |
| contents | The classic Lusternik--Schnirelmann theorem states that there are three distinct simple periodic geodesics on any Riemannian 2-sphere $M$. It has been proven by Y. Liokumovich, A. Nabutovsky and R. Rotman that the shortest three such curves have lengths bounded in terms of the diameter $d$ of $M$. We show that at any point $p$ on $M$ there exist at least two distinct simple geodesic loops (geodesic segments that start and end at $p$) whose lengths are respectively bounded by $8d$ and $14d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12673 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Short Simple Geodesic Loops on a 2-Sphere Beach, Isabel Differential Geometry 53C22 The classic Lusternik--Schnirelmann theorem states that there are three distinct simple periodic geodesics on any Riemannian 2-sphere $M$. It has been proven by Y. Liokumovich, A. Nabutovsky and R. Rotman that the shortest three such curves have lengths bounded in terms of the diameter $d$ of $M$. We show that at any point $p$ on $M$ there exist at least two distinct simple geodesic loops (geodesic segments that start and end at $p$) whose lengths are respectively bounded by $8d$ and $14d$. |
| title | Short Simple Geodesic Loops on a 2-Sphere |
| topic | Differential Geometry 53C22 |
| url | https://arxiv.org/abs/2407.12673 |