The horofunction compactification of Teichmüller spaces of surfaces with boundary

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• 作者：D. Alessandrini^a ; ^{daniele.alessandrini@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; L. Liu^b ; ^{mcsllx@mail.sysu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; A. Papadopoulos^c ; ^d ; ^{athanase.papadopoulos@math.unistra.fr" class="auth_mail" title="E-mail the corresponding author} ; W. Su^e ; ^{suwx@fudan.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：32G15 ; 30F30 ; 30F60
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 August 2016
• 年：2016
• 卷：208
• 期：Complete
• 页码：160-191
• 全文大小：590 K

文摘

The arc metric is an asymmetric metric on the Teichmüller space T(S)$\mathcal{T}(S)$ 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)$\mathcal{T}(S)$ 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.