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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On asymptotic Teichmüller space


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


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Additional Information

Alastair Fletcher
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email: Alastair.Fletcher@warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04944-7
PII: S 0002-9947(09)04944-7
Keywords: Asymptotic Teichm\"{u}ller space, little Bers space
Received by editor(s): February 29, 2008
Published electronically: December 2, 2009
Additional Notes: The author was supported by EPSRC grant EP/D065321/1
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.