|
Local boundary dilatation of quasiconformal maps in the disk
Authors:
Guizhen Cui and Yi Qi
Journal:
Proc. Amer. Math. Soc. 130 (2002), 1383-1389
MSC (2000):
Primary 30F60; Secondary 32G15
Posted:
October 17, 2001
MathSciNet review:
1879961
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
- 1.
G. Cui, Geometrically finite rational maps with given combinatorics, Preprint, Nov., 1999.
- 2.
Clifford
J. Earle and Curt
McMullen, Quasiconformal isotopies, Holomorphic functions and
moduli, Vol. I (Berkeley, CA, 1986) Math. Sci. Res. Inst. Publ.,
vol. 10, Springer, New York, 1988, pp. 143–154. MR 955816
(89h:30028), http://dx.doi.org/10.1007/978-1-4613-9602-4_12
- 3.
Richard
Fehlmann, Über extremale quasikonforme Abbildungen,
Comment. Math. Helv. 56 (1981), no. 4, 558–580
(German). MR
656212 (83e:30024), http://dx.doi.org/10.1007/BF02566227
- 4.
Frederick
P. Gardiner, Teichmüller theory and quadratic
differentials, Pure and Applied Mathematics (New York), John Wiley
& Sons Inc., New York, 1987. A Wiley-Interscience Publication. MR 903027
(88m:32044)
- 5.
Frederick
P. Gardiner and Nikola
Lakic, Quasiconformal Teichmüller theory, Mathematical
Surveys and Monographs, vol. 76, American Mathematical Society,
Providence, RI, 2000. MR 1730906
(2001d:32016)
- 6.
Olli
Lehto, Univalent functions and Teichmüller spaces,
Graduate Texts in Mathematics, vol. 109, Springer-Verlag, New York,
1987. MR
867407 (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.
Kurt
Strebel, On the existence of extremal Teichmueller mappings,
J. Analyse Math. 30 (1976), 464–480. MR 0440031
(55 #12912)
- 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
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
30F60,
32G15
Retrieve articles in all journals
with MSC (2000):
30F60,
32G15
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:
http://dx.doi.org/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
Article copyright:
© Copyright 2001 American Mathematical Society
|
