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

It is known that the Teichmuller distance on the universal Teichmuller 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 Teichmuller 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.