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...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
February 2016
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| In: |
Monatshefte für Mathematik
Year: 2016, Volume: 179, Issue: 2, Pages: 165-189 |
| ISSN: | 1436-5081 |
| DOI: | 10.1007/s00605-015-0813-9 |
| Online Access: | 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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| Author Notes: | D. Alessandrini, L. Liu, A. Papadopoulos, W. Su |
| Summary: | 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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| Item Description: | Published online: 29 August 2015 Gesehen am 09.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1436-5081 |
| DOI: | 10.1007/s00605-015-0813-9 |