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HAMILTON SEQUENCES FOR EXTREMAL QUASICONFORMAL MAPPINGS OF DOUBLY-CONNECTED DOMAINS

Part of: Geometric function theory

Published online by Cambridge University Press:  22 March 2013

GUOWU YAO
GUOWU YAO*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, PR China email gwyao@math.tsinghua.edu.cn
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Abstract

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Let $T(S)$ be the Teichmüller space of a hyperbolic Riemann surface $S$. Suppose that $\mu $ is an extremal Beltrami differential at a given point $\tau $ of $T(S)$ and $\{ {\phi }_{n} \} $ is a Hamilton sequence for $\mu $. It is an open problem whether the sequence $\{ {\phi }_{n} \} $ is always a Hamilton sequence for all extremal differentials in $\tau $. S. Wu [‘Hamilton sequences for extremal quasiconformal mappings of the unit disk’, Sci. China Ser. A 42 (1999), 1033–1042] gave a positive answer to this problem in the case where $S$ is the unit disc. In this paper, we show that it is also true when $S$ is a doubly-connected domain.

Keywords

Teichmüller spaceHamilton sequence

MSC classification

Secondary: 30C75: Extremal problems for conformal and quasiconformal mappings, other methods 30C62: Quasiconformal mappings in the plane
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 376 - 379
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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Wu, S., ‘Hamilton sequences for extremal quasiconformal mappings of the unit disk’, Sci. China Ser. A. 42 (1999), 1033–1042.CrossRefGoogle Scholar