Besicovitch-type inequality for closed geodesics on 2-dimensional spheres
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913888803487744 |
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| author | Talipov, Talant |
| author_facet | Talipov, Talant |
| contents | We prove the existence of a constant $C > 0$ such that for any Riemannian metric $g$ on a 2-dimensional sphere $S^2$, there exist two distinct closed geodesics with lengths $L_{1}$ and $L_{2}$ satisfying $L_{1} L_{2} \leq C \cdot \operatorname{Area}(S^2, g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Besicovitch-type inequality for closed geodesics on 2-dimensional spheres Talipov, Talant Differential Geometry 53C22 (Primary), 58E10, 51F99 We prove the existence of a constant $C > 0$ such that for any Riemannian metric $g$ on a 2-dimensional sphere $S^2$, there exist two distinct closed geodesics with lengths $L_{1}$ and $L_{2}$ satisfying $L_{1} L_{2} \leq C \cdot \operatorname{Area}(S^2, g)$. |
| title | Besicovitch-type inequality for closed geodesics on 2-dimensional spheres |
| topic | Differential Geometry 53C22 (Primary), 58E10, 51F99 |
| url | https://arxiv.org/abs/2412.02028 |