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On the analytic structure of certain infinite dimensional Teicmüller spaces

Published online by Cambridge University Press:  22 January 2016

Takeo Ohsawa
Takeo Ohsawa*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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It is well known since long time that quasiconformally different finite Riemann surfaces give rise to biholomorphically nonequivalent Teichmüller spaces except for a few obvious cases (cf. [R], [E-K]). This is deduced as an application of Royden’s theorem asserting that the Teichmüller metric is equal to the Kobayashi metric. For the case of infinite Riemann surfaces, however, it is still unknown whether or not the corresponding result holds, although it has been shown by F. Gardiner [G] that Royden’s theorem is also valid for the infinite dimensional Teichmüller spaces. On the other hand, recent activity of several mathematicians shows that the infinite dimensional Teichmüller spaces are interesting objects of complex analytic geometry (cf. [Kru], [T], [N], [E-K-K]). Therefore, based on the generalized form of Royden’s theorem, one might well look for further insight into Teichmüller spaces by studying the above mentioned nonequivalence question.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 143 - 156
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

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