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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 the Teichmüller theory of circle patterns


Authors: Zhengxu He and Jinsong Liu
Journal: Trans. Amer. Math. Soc. 365 (2013), 6517-6541
MSC (2010): Primary 30C35, 30C80
Published electronically: May 30, 2013
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Abstract: Given a circle pattern on the Riemann sphere $ \hat {\mathbb{C}}$, in this paper we prove that its quasiconformal deformation space can be naturally identified with the product of the Teichmüller spaces of its interstices.


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Additional Information

Zhengxu He
Affiliation: Institute of Mathematics, Academic of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China.
Address at time of publication: HUA Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: zhe00@earthlink.net

Jinsong Liu
Affiliation: Institute of Mathematics, Academic of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China.
Address at time of publication: HUA Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: liujsong@math.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05892-8
PII: S 0002-9947(2013)05892-8
Received by editor(s): October 13, 2011
Received by editor(s) in revised form: May 31, 2012
Published electronically: May 30, 2013
Additional Notes: The second author was supported by the National Natural Science Foundation of China (Grant No. 10831004).
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.