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Decomposing diffeomorphisms of the sphere

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.

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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.

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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.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/G050120/1
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification: 20H10 (primary)
Record Number:CaltechAUTHORS:20120622-134602277
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32046
Deposited By: Jason Perez
Deposited On:22 Jun 2012 21:30
Last Modified:09 Nov 2021 20:03

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