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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The limiting shape of one-dimensional Teichmüller spaces


Author: Toshiyuki Sugawa
Journal: Proc. Amer. Math. Soc. 136 (2008), 2849-2858
MSC (2000): Primary 30F60; Secondary 30F30, 30C62
Published electronically: March 21, 2008
MathSciNet review: 2399050
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Abstract: We show that the Bers embedding of the Teichmüller space of a once-punctured torus converges to the cardioid in the sense of Carathéodory up to rotation when the base torus goes to the boundary of its moduli space.


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Additional Information

Toshiyuki Sugawa
Affiliation: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526 Japan
Address at time of publication: Division of Mathematics, Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
Email: sugawa@math.sci.hiroshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09428-8
PII: S 0002-9939(08)09428-8
Keywords: Cardioid, Teichm\"uller space, holomorphic motion, once-punctured torus
Received by editor(s): March 14, 2007
Published electronically: March 21, 2008
Additional Notes: The author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039.
Communicated by: Mario Bonk
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.