Título:
Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
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Autor:
Alvarez, Sébastien
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Tipo de documento:
Preprint
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Descriptores:
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - DYNAMICAL SYSTEMS
MATHEMATICS - DYNAMICAL SYSTEMS
Año de publicación:
2025
Contenido:
Resumen:
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.
Descripción:
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arXiv
EN:
Mathematics (Differential Geometry), arXiv:2502.07626, feb. 2025, pp. 1-29
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Citación:
Alvarez, S. "Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces".[Prerint] Publicado en: Mathematics (Differential Geometry). arXiv:2502.07626, feb. 2025, pp.1-29. DOI: 10.48550/arXiv.2502.07626
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2502.07626v1.pdf | — | 381.69 KB | Adobe PDF |