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The limiting shape of one-dimensional Teichmüller spaces
Author(s):
Toshiyuki
Sugawa
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2849-2858.
MSC (2000):
Primary 30F60;
Secondary 30F30, 30C62
Posted:
March 21, 2008
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Additional information
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.
References:
-
- 1.
- L. V. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385-404. MR 0115006 (22:5813)
- 2.
- A. F. Beardon and Ch. Pommerenke, The Poincaré metric of plane domains, J. London Math. Soc. (2) 18 (1978), 475-483. MR 518232 (80a:30020)
- 3.
- L. Bers, On boundaries of Teichmüller spaces and on Kleinian groups: I, Ann. of Math. (2) 91 (1970), 570-600. MR 0297992 (45:7044)
- 4.
- F. P. Gardiner and N. Lakic, Quasiconformal Teichmüller Theory, Amer. Math. Soc., Providence, RI, 2000.MR 1730906 (2001d:32016)
- 5.
- D. A. Hejhal, Universal covering maps for variable regions, Math. Z. 137 (1974), 7-20. MR 0349989 (50:2482)
- 6.
- C. I. Kalme, Remarks on a paper by Lipman Bers, Ann. of Math. (2) 91 (1970), 601-606. MR 0272998 (42:7879)
- 7.
- Y. Komori and T. Sugawa, Bers embedding of the Teichmüller space of a once-punctured torus, Conform. Geom. Dyn. 8 (2004), 115-142. MR 2060380 (2005g:30055)
- 8.
- Y. Komori, T. Sugawa, M. Wada, and Y. Yamashita, Drawing Bers embeddings of the Teichmüller space of once-punctured tori, Exper. Math. 15 (2006), 51-60. MR 2229385 (2006m:30078)
- 9.
- G. McShane, Weierstrass points and simple geodesics, Bull. London Math. Soc. 36 (2004), 181-187. MR 2026411 (2004j:57023)
- 10.
- Y. Minsky, The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), 559-626. MR 1689341 (2000f:30028)
- 11.
- H. Miyachi, Cusps in complex boundaries of one-dimensional Teichmüller spaces, Conform. Geom. Dyn. 7 (2003), 103-151. MR 2023050 (2004j:30091)
- 12.
- S. Nag, The Complex Analytic Theory of Teichmüller Spaces, Wiley, New York, 1988. MR 927291 (89f:32040)
- 13.
- T. Nakanishi, A theorem on the outradii of Teichmüller spaces, J. Math. Soc. Japan 40 (1988), 1-8. MR 917391 (89e:30083)
- 14.
- W. C. Royster, On the univalence of a certain integral, Michigan Math. J. 12 (1965), 385-387. MR 0183866 (32:1342)
- 15.
- T. Sugawa, Estimates of hyperbolic metric with applications to Teichmüller spaces, Kyungpook Math. J. 42 (2002), 51-60. MR 1915906 (2003g:30084)
- 16.
- -, Cardioids and Teichmüller spaces, to appear in Proceedings of International Workshop on Teichmüller Theory and Moduli Problems, HRI, Allahabad, India (2006), Ramanujan Math. Soc. Lecture Notes Series in Mathematics.
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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:
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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