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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On asymptotic Teichmüller space
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by Alastair Fletcher PDF
Trans. Amer. Math. Soc. 362 (2010), 2507-2523 Request permission

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
  • MR Author ID: 749646
  • Email: Alastair.Fletcher@warwick.ac.uk
  • Received by editor(s): February 29, 2008
  • Published electronically: December 2, 2009
  • Additional Notes: The author was supported by EPSRC grant EP/D065321/1
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2507-2523
  • MSC (2010): Primary 30F60
  • DOI: https://doi.org/10.1090/S0002-9947-09-04944-7
  • MathSciNet review: 2584608