Kwakkel, Ferry and Markovic, V. (Vladimir). (2011) Quasiconformal homogeneity of genus zero surfaces. Journal d'Analyse Mathématique, Vol.113 (No.1). pp. 173-195. ISSN 0021-7670

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Abstract

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 D2, 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Quasiconformal mappings, Riemann surfaces
Journal or Publication Title:	Journal d'Analyse Mathématique
Publisher:	Magnes Press
ISSN:	0021-7670
Date:	2011
Volume:	Vol.113
Number:	No.1
Page Range:	pp. 173-195
Identification Number:	10.1007/s11854-011-0003-1
Status:	Peer Reviewed
Publication Status:	Published
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URI:	http://wrap.warwick.ac.uk/id/eprint/39051

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