Conformal currents and the entropy of negatively curved three-manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909210515603456 |
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| author | Marques, Fernando C. Neves, André |
| author_facet | Marques, Fernando C. Neves, André |
| contents | In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds.
We use this to prove some sharp bounds which involve the Liouville entropy of a negatively curved metric, the minimal surface entropy, and the area ratio. Using these ideas we also give a new proof of the Mostow Rigidity Theorem in the three-dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal currents and the entropy of negatively curved three-manifolds Marques, Fernando C. Neves, André Differential Geometry Dynamical Systems Geometric Topology 53A10, 57M50 In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds. We use this to prove some sharp bounds which involve the Liouville entropy of a negatively curved metric, the minimal surface entropy, and the area ratio. Using these ideas we also give a new proof of the Mostow Rigidity Theorem in the three-dimensional case. |
| title | Conformal currents and the entropy of negatively curved three-manifolds |
| topic | Differential Geometry Dynamical Systems Geometric Topology 53A10, 57M50 |
| url | https://arxiv.org/abs/2405.16302 |