Teichmueller Spaces with Asymptotic Conformal Equivalence. Preliminary Notes, May1995

摘要

In this article we extend some of the results known when R is the unit disk tothe case when R is an arbitrary Riemann surface. In particular, for any Riemann surface R, we show that T sub 0 are complex manifolds modelled on Banach spaces. Also, T sub 0 is connected and complete with respect to Teichmueller's metric an T and the quotient space T/T sub 0 with the quotient metric is also complete. The quotient metric has an infinitesimal form, and it is equal to the integral of its infinitesimal form. There is a principal of contraction for the quotient space T/T sub 0, exactly as in the case when R is the unit disk.