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. doi:10.1017/S002461150501573X. 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 | |||||||||
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| 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 | |||||||||
| DOI: | 10.1017/S002461150501573X | |||||||||
| 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: | 15 Nov 2021 17:29 |
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