On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space
This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
February 2016
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| In: |
Monatshefte für Mathematik
Year: 2016, Jahrgang: 179, Heft: 2, Pages: 165-189 |
| ISSN: | 1436-5081 |
| DOI: | 10.1007/s00605-015-0813-9 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1007/s00605-015-0813-9 Verlag, Volltext: https://link.springer.com/article/10.1007/s00605-015-0813-9 
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| Verfasserangaben: | D. Alessandrini, L. Liu, A. Papadopoulos, W. Su |
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| 245 | 1 | 0 | |a On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller space |c D. Alessandrini, L. Liu, A. Papadopoulos, W. Su |
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| 520 | |a This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or hyperbolic structure on S) and they also depend on the choice of a distance on the set of equivalence classes of marked hyperbolic structures. We address the question of the comparison between two deformation spaces, namely, the quasiconformal Teichmüller space and the length-spectrum Teichmüller space. There is a natural inclusion map of the quasiconformal space into the length-spectrum space, which is not always surjective. We work under the hypothesis that the basepoint (a hyperbolic surface) satisfies a condition we call “upper-boundedness”. This means that this surface admits a pants decomposition defined by curves whose lengths are bounded above. | ||
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