Quasiconformal Homogeneity of Genus Zero Surfaces

Ferry Kwakkel; Vlad Markovic

doi:10.1007/s11854-011-0003-1

paper

Quasiconformal Homogeneity of Genus Zero Surfaces

arXiv:0910.1050 · doi:10.1007/s11854-011-0003-1

Abstract

A Riemann surface $M$ is said to be $K$ -quasiconformally homogeneous if for every two points $p, q \in M$ , there exists a $K$ -quasiconformal homeomorphism $f : M \to M$ such that $f (p) = q$ . In this paper, we show there exists a universal constant $K_{0} > 1$ such that if $M$ is a $K$ -quasiconformally homogeneous hyperbolic genus zero surface other than the disk $D$ , then $K \geq K_{0}$ . This answers a question by Gehring and Palka.

Published in Journal d'Analyse Mathematique, Volume 113, Number 1, 173-195, 2011