TEICHMüLLER DISTANCE AND KOBAYASHI DISTANCE ON SUBSPACES OF THE UNIVERSAL TEICHMüLLER SPACE

摘要

It is known that the Teichmü ller distance on the universal Teichmü ller space T coincides with the Kobayashi distance. For a metric subspace of T having a comparable complex structure with that of T, we can similarly consider whether or not the Teichmü ller distance on the subspace coincides with the Kobayashi distance. In this paper, we give a sufficient condition for metric subspaces under which the problem above has a affirmative answer. Moreover, we introduce an example of such subspaces.