THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

2005 ◽  
Vol 26 (04) ◽  
pp. 537-542 ◽  
Author(s):  
ZHE WANG
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Universal Teichmüller Space

On Geodesics in Asymptotic Universal Teichmüller Space

2016 ◽  
Vol 59 (4) ◽  
pp. 1065-1074
Author(s):  
Zhou Zemin ◽  
Chen Jixiu
Keyword(s):  
Boundary Point ◽  
Teichmüller Space ◽  
Equivalence Classes ◽  
Necessary Condition ◽  
Teichmuller Space ◽  
Complex Dilatation ◽  
Universal Teichmüller Space

AbstractLet AT(Δ) be the asymptotic universal Teichmüller space, viewed as the space of all asymptotic Teichmüller equivalence classes [[μ]]. We show that ifμis asymptotically extremal in AT(Δ) andhp([[μ]]) <h([[μ]]) for some boundary pointpofΔ, then there are infinitely many geodesics joining [[0]] and [[μ]] in AT(Δ). As a corollary, a necessary condition for a complex dilatation to be uniquely extremal in AT(Δ) is given.

The asymptotic Teichmüller space and the asymptotic Grunsky map

2010 ◽  
Vol 140 (3) ◽  
pp. 651-672 ◽  
Author(s):  
Yuliang Shen
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Holomorphic Map ◽  
Universal Teichmüller Space ◽  
Kobayashi Metrics

The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper it is proved that the Grunsky map induces a holomorphic map on the asymptotic Teichmüller space. The Caratháodory and Kobayashi metrics on the asymptotic Teichmüller space are studied as applications.

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