The horofunction compactification of the arc metric on Teichmüller space

Abstract

The arc metric is an asymmetric metric on the Teichm{ü}ller space T(S) of a surface S with nonempty 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.

References in corpus (1)

• Maximally stretched laminations on geometrically finite hyperbolic manifolds

Cited by in corpus (3)

• Thurston's metric on Teichmüller space and the translation lengths of mapping classes
• On metrics defined by length spectra on Teichmuller spaces of surfaces with boundary
• The arc metric on Teichmüller spaces of surfaces of infinite type with boundary