Déformation localisée de surfaces de Riemann
Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T (X) of X. Furthermore, D has compact closure if and only if Y is simply connected or is...
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| Format: | article |
| Publication Date: | 2005 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | French |
| OAI Identifier: | oai:ddd.uab.cat:2053 |
| Online Access: | https://ddd.uab.cat/record/2053 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_49105_12 |
| Access Level: | Open access |
| Keyword: | Teichmüller theory Hyperbolic geometry Simple closed curves |
| Summary: | Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T (X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D = T (X) if and only if the components of X \ Y are all disks or punctured disks. |
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