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Unique extremality, local extremality and extremal non-decreasable dilatations

Published online by Cambridge University Press:  17 April 2009

Guowu Yao
Guowu Yao
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China e-mail: [email protected]
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Given a quasi-symmetric self-homeomorphism h of the unit circle Sl, let Q(h) be the set of all quasiconformal mappings with the boundary correspondence h. In this paper, it is shown that there exists certain quasi-symmetric homeomorphism h, such that Q(h) satisfies either of the conditions,

(1) Q(h) admits a quasiconformal mapping that is both uniquely locally-extremal and uniquely extremal-non-decreasable instead of being uniquely extremal;

(2) Q(h) contains infinitely many quasiconformal mappings each of which has an extremal non-decreasable dilatation.

An infinitesimal version of this result is also obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 321 - 329
Copyright
Copyright © Australian Mathematical Society 2007

References

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