On the first width of hyperbolic surfaces: multiplicity and lower bounds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917961182216192 |
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| author | Lima, Vanderson |
| author_facet | Lima, Vanderson |
| contents | On a closed Riemannian surface of negative curvature, we prove a characterization for configurations of closed geodesics arising from one parameter Allen-Cahn min-max constructions. One of the facts we conclude is that every geodesic occurs with multiplicity one. As an application we obtain a uniform sharp lower bound for the first min-max width of closed hyperbolic surfaces and prove it is only attained asymptotically. Moreover, we compute the first width of the Bolza surface and of some hyperbolic surfaces with small systoles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the first width of hyperbolic surfaces: multiplicity and lower bounds Lima, Vanderson Differential Geometry Analysis of PDEs On a closed Riemannian surface of negative curvature, we prove a characterization for configurations of closed geodesics arising from one parameter Allen-Cahn min-max constructions. One of the facts we conclude is that every geodesic occurs with multiplicity one. As an application we obtain a uniform sharp lower bound for the first min-max width of closed hyperbolic surfaces and prove it is only attained asymptotically. Moreover, we compute the first width of the Bolza surface and of some hyperbolic surfaces with small systoles. |
| title | On the first width of hyperbolic surfaces: multiplicity and lower bounds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2503.14846 |