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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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Some metrics on Teichmüller spaces of surfaces of infinite type
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by Lixin Liu and Athanase Papadopoulos PDF
Trans. Amer. Math. Soc. 363 (2011), 4109-4134 Request permission

Abstract:

Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topologically infinite type. These Teichmüller spaces first depend (set-theoretically) on whether we work in the hyperbolic category or in the conformal category. They also depend, given the choice of a point of view (hyperbolic or conformal), on the choice of a distance function on Teichmüller space. Examples of distance functions that appear naturally in the hyperbolic setting are the length spectrum distance and the bi-Lipschitz distance, and there are other useful distance functions. The Teichmüller spaces also depend on the choice of a basepoint. The aim of this paper is to present some examples, results and questions on the Teichmüller theory of surfaces of infinite topological type that do not appear in the setting of the Teichmüller theory of surfaces of finite type. In particular, we point out relations and differences between the various Teichmüller spaces associated to a given surface of topologically infinite type.
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Additional Information
  • Lixin Liu
  • Affiliation: Department of Mathematics, Sun Yat-sen (Zongshan) University, 510275, Guangzhou, People’s Republic of China
  • Email: mcsllx@mail.sysu.edu.cn
  • Athanase Papadopoulos
  • Affiliation: Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
  • MR Author ID: 135835
  • Email: papadopoulos@math.u-strasbg.fr
  • Received by editor(s): June 23, 2008
  • Received by editor(s) in revised form: March 16, 2009, and April 18, 2009
  • Published electronically: March 23, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 4109-4134
  • MSC (2000): Primary 32G15, 30F30, 30F60
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05090-7
  • MathSciNet review: 2792982