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Local boundary dilatation of quasiconformal maps in the disk
Author(s):
Guizhen
Cui;
Yi
Qi
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1383-1389.
MSC (2000):
Primary 30F60;
Secondary 32G15
Posted:
October 17, 2001
MathSciNet review:
1879961
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Abstract:
In this paper we partly give an affirmative answer to a problem proposed by F. Gardiner and N. Lakic by studying the gluing of quasiconformal maps.
References:
-
- 1.
- G. Cui, Geometrically finite rational maps with given combinatorics, Preprint, Nov., 1999.
- 2.
- C. Earle and C. McMullen, Quasiconformal isotopies, Holomorphic functions and Moduli, Vol. I, 143-154, edited by D. Drasin ect., Springer-Verlag, 1988. MR 89h:30028
- 3.
- R. Fehlman, Ueber extremale quasikonforme abbidungen, Comment. Math. Helv., 56(1981), 558-580. MR 83e:30024
- 4.
- F. Gardiner, Teichmuller theory and quadratic differentials, John Wiley and Sons, New York, 1987. MR 88m:32044
- 5.
- F. Gardiner and N. Lakic, Quasiconformal Teichmüller spaces, Math Surveys and Monographs, Vol 76, AMS., Providence, RI., 2000. MR 2001d:32016
- 6.
- O. Lehto, Univalent functions and Teichmüller spaces, GTM, Vol. 109, Springer-Verlag, New York, 1987. MR 88f:30073
- 7.
- Li, Z., Quasiconformal mappings with applications to Riemann surfaces (in Chinese), Science Press (1988).
- 8.
- Reich E. and Strebel K. Extremal quasiconformal mapping with given boundary values, Bull. Amer. Math. Soc. 79 (1973), 488-490.
- 9.
- Strebel, K., On the existence of extremal Teichmüller mappings, J. d'analyses Math., 30 (1976), 464-480. MR 55:12912
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Additional Information:
Guizhen
Cui
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Email:
gzcui@math08.math.ac.cn
Yi
Qi
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Address at time of publication:
Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Email:
qiyi@math03.math.ac.cn, yiqi1@yahoo.com
DOI:
10.1090/S0002-9939-01-06353-5
PII:
S 0002-9939(01)06353-5
Keywords:
Quasiconformal mapping,
Teichm\"uller space
Received by editor(s):
November 8, 2000
Posted:
October 17, 2001
Additional Notes:
This work was supported by the NSF Grant 19871084 and 19901032 of China and the China Postdoctoral Science Foundation
Communicated by:
Juha Heinonen
Copyright of article:
Copyright
2001,
American Mathematical Society
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