Abstract:We introduce a function model for the Teichmüller space of a closed hyperbolic Riemann surface. Then we introduce a new metric by using the maximum norm on the function space on the Teichmüller space. We prove that the identity map from the Teichmüller space equipped with the usual Teichmüller metric to the Teichmüller space equipped with this new metric is uniformly continuous. Furthermore, we also prove that the inverse of the identity, that is, the identity map from the Teichmüller space equipped with this … Show more
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