Quasiconformal homogeneity of genus zero surfaces

Author: 

Kwakkel, F
Markovic, V

Publication Date: 

1 January 2011

Journal: 

Journal d'Analyse Mathematique

Last Updated: 

2021-01-10T14:19:38.03+00:00

Issue: 

1

Volume: 

113

DOI: 

10.1007/s11854-011-0003-1

page: 

173-195

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. © 2011 Hebrew University Magnes Press.

Symplectic id: 

1110010

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article