On asymptotic Teichmüller space

Abstract

In this article we prove that for any hyperbolic Riemann surface M M of infinite analytic type, the little Bers space Q 0 ( M ) Q_{0}(M) is isomorphic to c 0 c_{0} . As a consequence of this result, if M M is such a Riemann surface, then its asymptotic Teichmüller space A T ( M ) AT(M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l ∞ / c 0 l^{\infty }/c_{0} . Further, if M M and N N are two such Riemann surfaces, their asymptotic Teichmüller spaces, A T ( M ) AT(M) and A T ( N ) AT(N) , are locally bi-Lipschitz equivalent.