On Teichmüller contraction

Author:
Frederick P. Gardiner

Journal:
Proc. Amer. Math. Soc. **118** (1993), 865-875

MSC:
Primary 30F60; Secondary 32G15

DOI:
https://doi.org/10.1090/S0002-9939-1993-1152277-1

MathSciNet review:
1152277

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Abstract: Universal Teichmüller space is the space of quasi-symmetric homeomorphisms of a circle factored by those Möbius transformations that preserve the circle. Another Teichmüller space, which also has universal properties, is factored by the closed subgroup of symmetric homeomorphisms. Teichmüller's metric for 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 . 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:
https://doi.org/10.1090/S0002-9939-1993-1152277-1

Article copyright:
© Copyright 1993
American Mathematical Society