Foliated Plateau problems, geometric rigidity and equidistribution of closed $k$-surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910822242975744 |
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| author | Alvarez, Sébastien |
| author_facet | Alvarez, Sébastien |
| contents | In this note, we survey recent advances in the study of dynamical properties of the space of surfaces with constant curvature in three-dimensional manifolds of negative sectional curvature. We interpret this space as a two-dimensional analogue of the geodesic flow and explore the extent to which the thermodynamic properties of the latter can be generalized to the surface setting. Additionally, we apply this theory to derive geometric rigidity results, including the rigidity of the hyperbolic marked area spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Foliated Plateau problems, geometric rigidity and equidistribution of closed $k$-surfaces Alvarez, Sébastien Differential Geometry Dynamical Systems In this note, we survey recent advances in the study of dynamical properties of the space of surfaces with constant curvature in three-dimensional manifolds of negative sectional curvature. We interpret this space as a two-dimensional analogue of the geodesic flow and explore the extent to which the thermodynamic properties of the latter can be generalized to the surface setting. Additionally, we apply this theory to derive geometric rigidity results, including the rigidity of the hyperbolic marked area spectrum. |
| title | Foliated Plateau problems, geometric rigidity and equidistribution of closed $k$-surfaces |
| topic | Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2502.07626 |