TY - JOUR
T1 - The horofunction compactification of Teichmüller spaces of surfaces with boundary
AU - Alessandrini, D.
AU - Liu, L.
AU - Papadopoulos, A.
AU - Su, W.
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
AB - 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.
KW - Arc metric
KW - Horofunction
KW - Thurston's asymmetric metric
KW - Thurston's compactification
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U2 - 10.1016/j.topol.2016.05.011
DO - 10.1016/j.topol.2016.05.011
M3 - Article
AN - SCOPUS:84969794089
SN - 0166-8641
VL - 208
SP - 160
EP - 191
JO - Topology and its Applications
JF - Topology and its Applications
ER -