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Quasiconformal homeomorphisms and the convex hull boundary
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UNSPECIFIED (2004) Quasiconformal homeomorphisms and the convex hull boundary. ANNALS OF MATHEMATICS, 159 (1). pp. 305336.
Full text not available from this repository, contact author.Abstract
We investigate the relationship between an open simplyconnected region Omega subset of S2 and the boundary Y of the hyperbolic convex hull in H3 of S2 \ Omega. A counterexample is given to Thurston's conjecture that these spaces are related by a 2quasiconformal homeomorphism which extends to the identity map on their common boundary, in the case when the homeomorphism is required to respect any group of Mobius transformations which preserves Q. We show that the best possible universal lipschitz constant for the nearest point retraction r : Omega > Y is 2. We find explicit universal constants 0 < c(2) < c(1), such that no pleating map which bends more than cl in some interval of unit length is an embedding, and such that any pleating map which bends less than c(2) in each interval of unit length is embedded. We show that every Kquasiconformal homeomorphism D2 > D2 is a (K, a(K))quasiisometry, where a(K) is an explicitly computed function. The multiplicative constant is best possible and the additive constant a(K) is best possible for some values of K.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Journal or Publication Title:  ANNALS OF MATHEMATICS  
Publisher:  ANN MATHEMATICS  
ISSN:  0003486X  
Official Date:  January 2004  
Dates: 


Volume:  159  
Number:  1  
Number of Pages:  32  
Page Range:  pp. 305336  
Publication Status:  Published 
Data sourced from Thomson Reuters' Web of Knowledge
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