Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces

Alvarez, Sébastien

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.

Detalles Bibliográficos
2025
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - DYNAMICAL SYSTEMS
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/54607
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author Alvarez, Sébastien
author_facet Alvarez, Sébastien
author_role author
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collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Alvarez Sébastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
dc.creator.none.fl_str_mv Alvarez, Sébastien
dc.date.accessioned.none.fl_str_mv 2026-04-24T17:40:03Z
dc.date.available.none.fl_str_mv 2026-04-24T17:40:03Z
dc.date.issued.none.fl_str_mv 2025
dc.description.abstract.none.fl_txt_mv 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.
dc.format.extent.es.fl_str_mv 29 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv 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
dc.identifier.doi.none.fl_str_mv 10.48550/arXiv.2502.07626
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/54607
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.none.fl_str_mv Mathematics (Differential Geometry), arXiv:2502.07626, feb. 2025, pp. 1-29
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.other.es.fl_str_mv MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - DYNAMICAL SYSTEMS
dc.title.none.fl_str_mv Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
dc.type.es.fl_str_mv Preprint
dc.type.none.fl_str_mv info:eu-repo/semantics/preprint
dc.type.version.none.fl_str_mv info:eu-repo/semantics/submittedVersion
description 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.
eu_rights_str_mv openAccess
format preprint
id COLIBRI_93cf80188f66bfa01e6aad0ef545e8a0
identifier_str_mv 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
10.48550/arXiv.2502.07626
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
network_acronym_str COLIBRI
network_name_str COLIBRI
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publishDate 2025
reponame_str COLIBRI
repository.mail.fl_str_mv karina.camps@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
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rights_invalid_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
spelling Alvarez Sébastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2026-04-24T17:40:03Z2026-04-24T17:40:03Z2025Alvarez, 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.2502.07626https://hdl.handle.net/20.500.12008/5460710.48550/arXiv.2502.07626In 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.Submitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2026-04-24T13:51:18Z No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2502.07626v1.pdf: 390854 bytes, checksum: 120012e721b457a8ee65e259f41476ae (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2026-04-24T13:52:55Z (GMT) No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2502.07626v1.pdf: 390854 bytes, checksum: 120012e721b457a8ee65e259f41476ae (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2026-04-24T17:40:03Z (GMT). No. of bitstreams: 2 license_rdf: 27293 bytes, checksum: d62648cf14c1e37917d392ac87012955 (MD5) 2502.07626v1.pdf: 390854 bytes, checksum: 120012e721b457a8ee65e259f41476ae (MD5) Previous issue date: 202529 h.application/pdfenengarXivMathematics (Differential Geometry), arXiv:2502.07626, feb. 2025, pp. 1-29Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)MATHEMATICS - DIFFERENTIAL GEOMETRYMATHEMATICS - DYNAMICAL SYSTEMSFoliated Plateau problems, geometric rigidity and equidistribution of closed K-surfacesPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAlvarez, SébastienLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/54607/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/54607/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
Alvarez, Sébastien
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - DYNAMICAL SYSTEMS
status_str submittedVersion
title Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
title_full Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
title_fullStr Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
title_full_unstemmed Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
title_short Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
title_sort Foliated Plateau problems, geometric rigidity and equidistribution of closed K-surfaces
topic MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - DYNAMICAL SYSTEMS
url https://hdl.handle.net/20.500.12008/54607

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