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On various Teichmüller spaces of a surface of infinite topological type


Authors: Daniele Alessandrini, Lixin Liu, Athanase Papadopoulos and Weixu Su
Journal: Proc. Amer. Math. Soc. 140 (2012), 561-574
MSC (2000): Primary 32G15, 30F30, 30F60
DOI: https://doi.org/10.1090/S0002-9939-2011-10918-3
Published electronically: June 7, 2011
MathSciNet review: 2846324
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate various Teichmüller spaces associated to a surface of infinite topological type. We show that the length spectrum metric is complete. We give results and examples that compare the length spectrum Teichmüller space with the quasiconformal and the Fenchel-Nielsen Teichmüller spaces.


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Additional Information

Daniele Alessandrini
Affiliation: (Daniele Alessandrini) Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Address at time of publication: Max-Plank-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany
Email: daniele.alessandrini@gmail.com

Lixin Liu
Affiliation: (Lixin Liu) Department of Mathematics, Sun Yat-sen (Zhongshan) University, 510275, Guangzhou, People’s Republic of China
Email: mcsllx@mail.sysu.edu.cn

Athanase Papadopoulos
Affiliation: (Athanase Papadopoulos) Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: athanase.papadopoulos@math.unistra.fr

Weixu Su
Affiliation: (Weixu Su) Department of Mathematics, Sun Yat-sen (Zhongshan) University, 510275, Guangzhou, People’s Republic of China
Email: su023411040@163.com

DOI: https://doi.org/10.1090/S0002-9939-2011-10918-3
Keywords: Surfaces of infinite topological type, Teichmüller space, Teichmüller metric, quasiconformal metric, length spectrum metric, Fenchel-Nielsen coordinates, Fenchel-Nielsen metric.
Received by editor(s): August 23, 2010
Received by editor(s) in revised form: November 22, 2010
Published electronically: June 7, 2011
Additional Notes: The second and fourth authors were partially supported by NSFC grants 10871211 and 11011130207.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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