The min-max width of spheres associated to the distance function
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916653748453376 |
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| author | Montezuma, Rafael Ribeiro, Idalina |
| author_facet | Montezuma, Rafael Ribeiro, Idalina |
| contents | What one obtains when the min-max methods for the distance function are applied on the space of pairs of points of a Riemannian two-sphere? This question is studied in details in the present article. We show that the associated min-max width do not always coincide with half of the length of a simple closed geodesic which is the union of two minimizing geodesics with the same endpoints. Therefore, it is a new geometric invariant. We study the structure of the set of minimizing geodesics joining a pair of points realizing the width, and relationships between this invariant and the diameter. The extrinsic case of an embedded Riemannian sphere is also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The min-max width of spheres associated to the distance function Montezuma, Rafael Ribeiro, Idalina Differential Geometry What one obtains when the min-max methods for the distance function are applied on the space of pairs of points of a Riemannian two-sphere? This question is studied in details in the present article. We show that the associated min-max width do not always coincide with half of the length of a simple closed geodesic which is the union of two minimizing geodesics with the same endpoints. Therefore, it is a new geometric invariant. We study the structure of the set of minimizing geodesics joining a pair of points realizing the width, and relationships between this invariant and the diameter. The extrinsic case of an embedded Riemannian sphere is also considered. |
| title | The min-max width of spheres associated to the distance function |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.12477 |