ON THE THURSTON BOUNDARY AND THE RELATIVELY spacing diaeresis HYPERBOLIC BOUNDARY OF TEICHMULLER SPACE

We obtain a result about the relation between the Thurston boundary and the relatively hyperbolic boundary of Teichmuiller space. Precisely, we prove that the identity map on Teichmuiller space extends to a continuous surjective map from the subset of the Thurston boundary consisting of minimal measured foliations to the relatively hyperbolic boundary. As an application, to relate the Thurston com-pactification and the Teichmuiller compactification of Teichmuiller space, we construct a new compactification of Teichmuiller space which is weaker than the Thurston com-pactification and the Teichmuiller compactification.