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Quasiconformal homogeneity of genus zero surfaces
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Kwakkel, Ferry and Markovic, V. (Vladimir) (2011) Quasiconformal homogeneity of genus zero surfaces. Journal d'Analyse Mathématique, Vol.113 (No.1). pp. 173-195. doi:10.1007/s11854-011-0003-1 ISSN 0021-7670.
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Official URL: http://dx.doi.org/10.1007/s11854-011-0003-1
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, Engineering and Medicine > 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 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.113 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 173-195 | ||||
| DOI: | 10.1007/s11854-011-0003-1 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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