Fletcher, Alastair and Markovic, Vladimir (2012) Decomposing diffeomorphisms of the sphere. Bulletin of the London Mathematical Society, 44 (3). pp. 599-609. ISSN 0024-6093. doi:10.1112/blms/bdr111. https://resolver.caltech.edu/CaltechAUTHORS:20120622-134602277
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Abstract
A central problem in the theory of quasiconformal and bi-Lipschitz mappings is whether they can be written as a composition of such mappings with small distortion. In this paper, we prove a decomposition result for C^1 diffeomorphisms of the sphere; namely, we show that, given ε>0, every C^1 diffeomorphism of the sphere S^n can be written as a composition of bi-Lipschitz mappings with isometric distortion at most 1 + ε.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2011 London Mathematical Society. Received 20 September 2010; revised 22 June 2011; published online 25 November 2011. The first author was supported by EPSRC grant EP/G050120/1. The authors would like to thank the anonymous referee for some very useful comments, which have improved the readability of the paper, and for suggesting some references for inclusion. | |||||||||
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| Issue or Number: | 3 | |||||||||
| Classification Code: | 2010 Mathematics Subject Classification: 20H10 (primary) | |||||||||
| DOI: | 10.1112/blms/bdr111 | |||||||||
| Record Number: | CaltechAUTHORS:20120622-134602277 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120622-134602277 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32046 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Jason Perez | |||||||||
| Deposited On: | 22 Jun 2012 21:30 | |||||||||
| Last Modified: | 09 Nov 2021 20:03 |
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