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On asymptotic Teichmüller space

Author(s): Alastair Fletcher
Journal: Trans. Amer. Math. Soc. 362 (2010), 2507-2523.
MSC (2010): Primary 30F60
Posted: December 2, 2009
MathSciNet review: 2584608
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Abstract: In this article we prove that for any hyperbolic Riemann surface of infinite analytic type, the little Bers space $Q_{0}(M)$ is isomorphic to $c_{0}$ . As a consequence of this result, if is such a Riemann surface, then its asymptotic Teichmüller space is bi-Lipschitz equivalent to a bounded open subset of the Banach space $l^{\infty}/c_{0}$ . Further, if and are two such Riemann surfaces, their asymptotic Teichmüller spaces, and , are locally bi-Lipschitz equivalent.

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