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Convex Regions in the Plane and their Domes

Epstein, D. B. A. and Marden, A. and Markovic, V. (2006) Convex Regions in the Plane and their Domes. Proceedings of the London Mathematical Society, 92 (03). pp. 624-654. ISSN 0024-6115. https://resolver.caltech.edu/CaltechAUTHORS:20170508-091514221

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Abstract

We make a detailed study of the relation of a euclidean convex region Ω ⊂ C → Dome (Ω). The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of Ω. The first result is to prove that the nearest point retraction r: Ω → Dome (Ω) is 2-quasiconformal. The second is to establish precise estimates of the distortion of r near ∂ Ω.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/S002461150501573XDOIArticle
http://onlinelibrary.wiley.com/doi/10.1017/S002461150501573X/abstractPublisherArticle
Additional Information:© 2006 London Mathematical Society. Received 18 August 2004; revised 11 July 2005.
Issue or Number:03
Classification Code:2000 Mathematics Subject Classification: 30C75, 30F40, 30F45, 30F60
Record Number:CaltechAUTHORS:20170508-091514221
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170508-091514221
Official Citation:Epstein, D. B. A., Marden, A. and Markovic, V. (2006), Convex Regions in the Plane and their Domes. Proceedings of the London Mathematical Society, 92: 624–654. doi:10.1017/S002461150501573X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77250
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 May 2017 21:50
Last Modified:03 Oct 2019 17:55

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