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Quasiconformal homogeneity of genus zero surfaces

Kwakkel, Ferry and Markovic, Vladimir (2011) Quasiconformal homogeneity of genus zero surfaces. Journal d'Analyse Mathématique, 113 (1). pp. 173-195. ISSN 0021-7670.

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A Riemann surface M is said to be K-quasiconformally homogeneous if, for every two points p, q ∈ M, there exists a K-quasiconformal homeomorphism f: M→M such that f(p) = q. In this paper, we show there exists a universal constant K > 1 such that if M is a K-quasiconformally homogeneous hyperbolic genus zero surface other than ⅅ^2, then K ≥ K. This answers a question by Gehring and Palka [10]. Further, we show that a non-maximal hyperbolic surface of genus g ≥ 1 is not K-quasiconformally homogeneous for any finite K ≥ 1.

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Additional Information:© 2011 Hebrew University Magnes Press. Received: 17 September 2009; First Online: 17 April 2011. The first author was supported by Marie Curie grant MRTN-CT-2006-035651 (CODY). The authors thank the referee for several useful suggestions and comments on the manuscript.
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Marie Curie FellowshipMRTN-CT-2006-035651 (CODY)
Issue or Number:1
Record Number:CaltechAUTHORS:20170508-143630640
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Official Citation:Kwakkel, F. & Markovic, V. JAMA (2011) 113: 173. doi:10.1007/s11854-011-0003-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77265
Deposited By: Tony Diaz
Deposited On:15 May 2017 19:41
Last Modified:03 Oct 2019 17:55

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