Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866913936440295424 |
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| author | Beach, Isabel |
| author_facet | Beach, Isabel |
| contents | We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk $M$ with convex boundary. The lengths of these curves are bounded in terms of the length of $\partial M$, the diameter of $M$, and the area of $M$. We also prove the existence of a short, simple geodesic chord on any Riemannian 2-disk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary Beach, Isabel Differential Geometry 53C22 We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk $M$ with convex boundary. The lengths of these curves are bounded in terms of the length of $\partial M$, the diameter of $M$, and the area of $M$. We also prove the existence of a short, simple geodesic chord on any Riemannian 2-disk. |
| title | Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary |
| topic | Differential Geometry 53C22 |
| url | https://arxiv.org/abs/2507.07797 |