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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.01626 |
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| _version_ | 1866929310093279232 |
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| author | Ammann, Bernd Loeh, Clara |
| author_facet | Ammann, Bernd Loeh, Clara |
| contents | A minimal geodesic on a Riemannian manifold is a geodesic defined on $\mathbb{R}$ that lifts to a globally distance minimizing curve on the universal covering. Bangert proved that there is a lower bound for the number of geometrically distinct minimal geodesics of closed Riemannian manifolds that is linear in the first Betti number, using the stable norm unit ball on the first homology. We refine this method to obtain a quadratic lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01626 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A quadratic lower bound for the number of minimal geodesics Ammann, Bernd Loeh, Clara Differential Geometry A minimal geodesic on a Riemannian manifold is a geodesic defined on $\mathbb{R}$ that lifts to a globally distance minimizing curve on the universal covering. Bangert proved that there is a lower bound for the number of geometrically distinct minimal geodesics of closed Riemannian manifolds that is linear in the first Betti number, using the stable norm unit ball on the first homology. We refine this method to obtain a quadratic lower bound. |
| title | A quadratic lower bound for the number of minimal geodesics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2311.01626 |