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

 

Conjugacies between rational maps and extremal quasiconformal maps


Author: Guizhen Cui
Journal: Proc. Amer. Math. Soc. 129 (2001), 1949-1953
MSC (2000): Primary 37F30, 30C75
Published electronically: February 22, 2001
MathSciNet review: 1825901
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Abstract:

We show that two rational maps which are $K$-quasiconformally combinatorially equivalent are $K$-quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.


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Additional Information

Guizhen Cui
Affiliation: Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: gzcui@math08.math.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05918-4
PII: S 0002-9939(01)05918-4
Keywords: Rational map, extremal quasiconformal map
Received by editor(s): August 21, 1999
Published electronically: February 22, 2001
Additional Notes: This work is supported by the National Natural Sience Foundation of China (No. 19871084)
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society