On asymptotic Teichmüller space

Abstract

In this article we prove that for any hyperbolic Riemann surface M of infinite analytic type, the little Bers space Q0(M) is isomorphic to c0. As a consequence of this result, if M is such a Riemann surface, then its asymptotic Teichm¨uller space AT(M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l∞/c0. Further, if M and N are two such Riemann surfaces, their asymptotic Teichm¨uller spaces, AT(M) and AT(N), are locally bi-Lipschitz equivalen