The horofunction compactification of Teichmüller spaces of surfaces with boundary

D. Alessandrini, L. Liu, A. Papadopoulos, W. Su

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)160-191
Number of pages32
JournalTopology and its Applications
Volume208
DOIs
StatePublished - 1 Aug 2016

Keywords

  • Arc metric
  • Horofunction
  • Thurston's asymmetric metric
  • Thurston's compactification

Fingerprint

Dive into the research topics of 'The horofunction compactification of Teichmüller spaces of surfaces with boundary'. Together they form a unique fingerprint.

Cite this