A Basmajian-type inequality for Riemannian surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929739294310400 |
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| author | Balacheff, Florent Fisac, David |
| author_facet | Balacheff, Florent Fisac, David |
| contents | We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic the relationship between orthospectrum and boundary length. More precisely, we establish a uniform lower bound on the boundary length in terms of the orthospectrum when fixing a metric invariant of the surface related to the classical notion of volume entropy. This inequality can be thought of as a Riemannian analog of Basmajian's identity for hyperbolic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03182 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Basmajian-type inequality for Riemannian surfaces Balacheff, Florent Fisac, David Differential Geometry Geometric Topology Primary: 53C23, 53C22. Secondary: 57K20 We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic the relationship between orthospectrum and boundary length. More precisely, we establish a uniform lower bound on the boundary length in terms of the orthospectrum when fixing a metric invariant of the surface related to the classical notion of volume entropy. This inequality can be thought of as a Riemannian analog of Basmajian's identity for hyperbolic surfaces. |
| title | A Basmajian-type inequality for Riemannian surfaces |
| topic | Differential Geometry Geometric Topology Primary: 53C23, 53C22. Secondary: 57K20 |
| url | https://arxiv.org/abs/2311.03182 |