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

 

On Teichmüller contraction


Author: Frederick P. Gardiner
Journal: Proc. Amer. Math. Soc. 118 (1993), 865-875
MSC: Primary 30F60; Secondary 32G15
MathSciNet review: 1152277
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Abstract: Universal Teichmüller space is the space of quasi-symmetric homeomorphisms $ QS$ of a circle factored by those Möbius transformations that preserve the circle. Another Teichmüller space, which also has universal properties, is $ QS$ factored by the closed subgroup $ S$ of symmetric homeomorphisms. Teichmüller's metric for $ QS\,\bmod S$ is the boundary dilatation metric. Sullivan's coiling property for Beltrami lines and the Hamilton-Reich-Strebel necessary and sufficient condition for extremality are proved for $ QS\bmod S$. The coiling property implies a contraction principle for certain types of self-mappings of Teichmüller space. It is also shown that the boundary dilatation metric has an infinitesimal form and that this metric is the integral of its infinitesimal form.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152277-1
PII: S 0002-9939(1993)1152277-1
Article copyright: © Copyright 1993 American Mathematical Society