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Convex regions in the plane and their domes
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Epstein, D. B. A., Marden, A. and Markovic, V. (Vladimir). (2006) Convex regions in the plane and their domes. Proceedings of the London Mathematical Society, Vol.92 (No.3). pp. 624654. ISSN 00246115

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Official URL: http://dx.doi.org/10.1017/S002461150501573X
Abstract
We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Convex domains, Convex geometry, Geometry, Hyperbolic, Geometry, Plane, Algebraic number theory  
Journal or Publication Title:  Proceedings of the London Mathematical Society  
Publisher:  Cambridge University Press  
ISSN:  00246115  
Official Date:  May 2006  
Dates: 


Volume:  Vol.92  
Number:  No.3  
Page Range:  pp. 624654  
Identification Number:  10.1017/S002461150501573X  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
References:  1. D. B. A. Epstein and A. Marden, ‘Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces’, Analytical and geometric aspects of hyperbolic space (ed. D. B. A. Epstein), London Mathematical Society Lecture Note Series 111 (Cambridge University Press, 1987) 113–253. 

URI:  http://wrap.warwick.ac.uk/id/eprint/696 
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