The horofunction compactification of the arc metric on Teichmuller space

The arc metric is an asymmetric metric on the Teichm{u}ller space T(S) of a surface S with nonempty boundary. In this paper we study the relation between Thurstons 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.