Approximation of infinite-dimensional Teichmüller spaces

Gardiner, Frederick P.

doi:10.1090/S0002-9947-1984-0728718-7

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Approximation of infinite-dimensional Teichmüller spaces

Author: Frederick P. Gardiner
Journal: Trans. Amer. Math. Soc. 282 (1984), 367-383
MSC: Primary 30F35; Secondary 30C70, 32G15, 32H15
MathSciNet review: 728718
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Abstract: By means of an exhaustion process it is shown that Teichmüller's metric and Kobayashi's metric are equal for infinite dimensional Teichmüller spaces. By the same approximation method important estimates coming from the Reich-Strebel inequality are extended to the infinite dimensional cases. These estimates are used to show that Teichmüller's metric is the integral of its infinitesimal form. They are also used to give a sufficient condition for a sequence to be an absolute maximal sequence for the Hamilton functional. Finally, they are used to give a new sufficient condition for a sequence of Beltrami coefficients to converge in the Teichmüller metric.

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