|
On invariant distances on asymptotic Teichmüller spaces
Author:
Hideki Miyachi
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1917-1925
MSC (2000):
Primary 32G15, 30F25, 30F60
Posted:
December 16, 2005
MathSciNet review:
2215119
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper, we will establish that any invariant distance on asymptotic Teichmüller space is a complete distance.
References
- 1.
Ahlfors L.V. and Weill G., A uniqueness theorem for Beltrami equations, Proc. Amer. Math. Soc. 13 (1962), 385-404. MR 0148896 (26:6393)
- 2.
Ahlfors L.V. and Sario L., Riemann surfaces, Princeton University Press (1960). MR 0114911 (22:5729)
- 3.
Dineen S., The Schwarz Lemma, Oxford Mathematical Monographs, Clarendon Press (1989). MR 1033739 (91f:46064)
- 4.
Earle C., On the Carathéodory metric in Teichmüller spaces, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Ann. of Math. Studies 79, Princeton Univ. Press (1974), 99-103. MR 0352450 (50:4937)
- 5.
Earle C.J., Gardiner F. and Lakic N., Asymptotic Teichmüller space, Part I: The complex structure, Comtemp. Math. 256 (2000), 17-38. MR 1759668 (2001m:32029)
- 6.
Earle C.J., Gardiner F. and Lakic N., Asymptotic Teichmüller space, Part II: The metric structure, Contemporary Math. 355 (2004), 187-219. MR 1759668 (2001m:32029)
- 7.
Earle C.J., Gardiner F. and Lakic N., Finsler structures and their quotients on domains in Banach spaces, Complex Dynamics and Related Topics, IP, New Studies in Math 5 (2004), 30-49.
- 8.
Earle C.J., Markovic J. and Saric D., Barycentric extension and the Bers embedding for asymptotic Teichmüller space, Comtemp. Math. 311 (2002), 85-105. MR 1940165 (2003i:30072)
- 9.
Franzoni T. and Vesentini E., Holomorphic maps and Invariant distances, Notas de Matemática, 69. North-Holland Publishing Co., Amsterdam, New York (1980). MR 0563329 (82a:32032)
- 10.
Gardiner F., The Teichmüller-Kobayashi metric for infinite-dimensional complex Teichmüller spaces. Kleinian groups and related topics (Oaxtepec, 1981), Lecture Notes in Math. 971, Springer, Berlin, New York (1983), pp. 48-67. MR 0690278 (84f:32025)
- 11.
Gardiner F. and Lakic N., Quasiconformal Teichmüller theory, Mathematical Surveys and Monographs 76, American Mathematical Society (2000). MR 1730906 (2001d:32016)
- 12.
Imayoshi Y. and Taniguchi M., An introduction to Teichmüller spaces, Springer-Verlag, Tokyo (1992). MR 1215481 (94b:32031)
- 13.
Nag S., The Complex Analytic Theory of Teichmüller spaces, Wiley-Interscience, New York (1998). MR 0927291 (89f:32040)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
32G15,
30F25,
30F60
Retrieve articles in all journals
with MSC (2000):
32G15,
30F25,
30F60
Additional Information
Hideki Miyachi
Affiliation:
Department of Mathematical Sciences, Tokyo Denki University, Ishizaka, Hatoyama, Hiki Saitama, 359-0394, Japan
Email:
miyachi@r.dendai.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08188-8
PII:
S 0002-9939(05)08188-8
Received by editor(s):
July 16, 2004
Received by editor(s) in revised form:
February 1, 2005
Posted:
December 16, 2005
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
|
