A theorem of Bers and Greenberg for infinite dimensional Teichmüller spaces

1988 ◽  
pp. 195-205 ◽  
Author(s):  
Frederick P. Gardiner
Keyword(s):  
Teichmüller Spaces ◽  
Infinite Dimensional ◽  
Teichmuller Spaces

scholarly journals On the analytic structure of certain infinite dimensional Teicmüller spaces

1996 ◽  
Vol 141 ◽  
pp. 143-156 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Riemann Surfaces ◽  
Analytic Structure ◽  
Kobayashi Metric ◽  
Teichmüller Spaces ◽  
Infinite Dimensional ◽  
Teichmuller Spaces ◽  
Teichmüller Metric ◽  
Long Time ◽  
Recent Activity ◽  
Insight Into

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.

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