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Characterisation of plane regions that support quasiconformal mappings to their domes

Marden, A. and Marković, V. (2007) Characterisation of plane regions that support quasiconformal mappings to their domes. Bulletin of the London Mathematical Society, 39 (6). pp. 962-972. ISSN 0024-6093. https://resolver.caltech.edu/CaltechAUTHORS:20170505-145802007

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Abstract

We prove that the nearest point retraction of a region P, not the whole plane, to its dome is long-range bilipschitz if and only if P is uniformly perfect. From this we prove that P uniformly perfect is necessary and sufficient for the existence of a K-quasiconformal map from P to its dome which extends to be the identity on the boundary and is finite distance to the nearest point retraction. Thus our work extends the classic theorem of Sullivan for simply-connected regions to regions of arbitrary connectivity. In particular, our study results in a simple, transparent proof of the original theorem.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1112/blms/bdm101DOIArticle
http://onlinelibrary.wiley.com/doi/10.1112/blms/bdm101/abstractPublisherArticle
Additional Information:© 2007 London Mathematical Society. Received 12 February 2007; published online 11 December 2007.
Issue or Number:6
Classification Code:2000 Mathematics Subject Classification: 30F (primary), 30C62, 30F40, 30F60, 32G05 (secondary)
Record Number:CaltechAUTHORS:20170505-145802007
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170505-145802007
Official Citation:Marden, A. and Markovic, V. (2007), Characterisation of plane regions that support quasiconformal mappings to their domes. Bulletin of the London Mathematical Society, 39: 962–972. doi:10.1112/blms/bdm101
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77238
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 May 2017 22:35
Last Modified:03 Oct 2019 17:55

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