The horofunction compactification of the arc metric on Teichm\"uller   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 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. 
Daniele Alessandrini, Lixin Liu, Athanase Papadopoulos (IRMA), Weixu   Su
math.GT