The horofunction compactification of Teichmüller spaces of surfaces with boundary
The arc metric is an asymmetric metric on the Teichmüller space T(S) of a surface S with nonempty boundary. It is the analogue of Thurston's metric on the Teichmüller space of a surface without boundary. In this paper we study the relation between Thurston's compactification and the horo...
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| Format: | Article (Journal) |
| Language: | English |
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25 May 2016
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| In: |
Topology and its applications
Year: 2016, Volume: 208, Pages: 160-191 |
| DOI: | 10.1016/j.topol.2016.05.011 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1016/j.topol.2016.05.011 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S016686411630092X 
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| Author Notes: | D. Alessandrini, L. Liu, A. Papadopoulos, W. Su |
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| 520 | |a The arc metric is an asymmetric metric on the Teichmüller space T(S) of a surface S with nonempty boundary. It is the analogue of Thurston's metric on the Teichmüller space of a surface without boundary. In this paper we study the relation between Thurston's compactification and the horofunction compactification of T(S) endowed with the arc metric. We prove that there is a natural homeomorphism between the two compactifications. This generalizes a result of Walsh [20] that concerns Thurston's metric. | ||
| 650 | 4 | |a Arc metric | |
| 650 | 4 | |a Horofunction | |
| 650 | 4 | |a Thurston's asymmetric metric | |
| 650 | 4 | |a Thurston's compactification | |
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