On Teichmuller Spaces for Finitely Generated Fuchsian Groups

1969 ◽  
Vol 91 (1) ◽  
pp. 67 ◽  
Author(s):  
Irwin Kra
Keyword(s):  
Fuchsian Groups ◽  
Finitely Generated ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces

On Ruelle’s property

2021 ◽  
pp. 1-13
Author(s):  
SHENGJIN HUO ◽  
MICHEL ZINSMEISTER
Keyword(s):  
Fuchsian Group ◽  
Fuchsian Groups ◽  
Finitely Generated ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Negative Results ◽  
Convergence Type ◽  
Mostow Rigidity

Abstract In this paper we investigate the range of validity of Ruelle’s property. First, we show that every finitely generated Fuchsian group has Ruelle’s property. We also prove the existence of an infinitely generated Fuchsian group satisfying Ruelle’s property. Concerning the negative results, we first generalize Astala and Zinsmeister’s results [Mostow rigidity and Fuchsian groups. C. R. Math. Acad. Sci. Paris311 (1990), 301–306; Teichmüller spaces and BMOA. Math. Ann.289 (1991), 613–625] by proving that all convergence-type Fuchsian groups of the first kind fail to have Ruelle’s property. Finally, we give some results about second-kind Fuchsian groups.

scholarly journals On Teichmüller Spaces of Koebe Groups

1997 ◽  
Vol 08 (05) ◽  
pp. 611-632
Author(s):  
Pablo Arés Gastesi
Keyword(s):  
Teichmüller Space ◽  
Universal Covering ◽  
Kleinian Groups ◽  
Fuchsian Groups ◽  
Teichmuller Space ◽  
Isomorphism Theorem ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Covering Group

In this paper we study the Teichmüller space of constructible Koebe groups. These are Kleinian groups arising from planar covering of 2-orbifolds. In the first part, we parametrize the Teichmüller spaces of Koebe groups using a technique that can be applied to explicitly compute generators of these groups, maybe by programming a computer. In the second part, we study some properties of these Teichmüller spaces. More precisely, we find the covering group of these spaces (the universal covering is the Teichmüller space of the punctured surface), and prove an isomorphism theorem similar to the Bers–Greenberg theorem for Fuchsian groups.

Teichmüller spaces for pointed Fuchsian groups

2010 ◽  
Vol 53 (8) ◽  
pp. 2031-2038
Author(s):  
MingFeng Sun ◽  
YuLiang Shen
Keyword(s):  
Fuchsian Groups ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces
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