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Characterisation of plane regions that support quasiconformal mappings to their domes
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Marden, A. and Markovic, V. (2007) Characterisation of plane regions that support quasiconformal mappings to their domes. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 39 (Part 6). pp. 962-972. doi:10.1112/blms/bdm101 ISSN 0024-6093.
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Official URL: http://dx.doi.org/10.1112/blms/bdm101
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: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Journal or Publication Title: | BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | ||||
| Publisher: | OXFORD UNIV PRESS | ||||
| ISSN: | 0024-6093 | ||||
| Official Date: | December 2007 | ||||
| Dates: |
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| Volume: | 39 | ||||
| Number: | Part 6 | ||||
| Number of Pages: | 11 | ||||
| Page Range: | pp. 962-972 | ||||
| DOI: | 10.1112/blms/bdm101 | ||||
| Publication Status: | Published |
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