A NEW COMPACTIFICATION OF TEICHMÜLLER SPACE

Abstract

We construct a new compactification of Teichmüller space. We prove that this new compactification is finer than the Gardiner–Masur compactification of Teichmüller space and the action of the mapping class group on Teichmüller space extends continuously to this new compactification. We also construct some special points in the new boundary. The construction of the new compactification is based on the Hubbard-Masur theorem, which states that there is an one-to-one corresponding between holomorphic differentials and measured foliations