Quasiconformal Homogeneity of Genus Zero Surfaces

Details Quasiconformal Homogeneity of Genus Zero Surfaces Quasiconformal Homogeneity of Genus Zero Surfaces

2009-10-06

arxiv.org/abs/0910.1050v3

JOURNAL D'ANALYSE MATH\'EMATIQUE, Volume 113, Number 1, 173-195, 2011

Mathematics

Geometric Topology

Replaced v1 as some pictures and a reference were not rendered correctly Replaced v2: v3 will appear in Journal d'Analyse Math

Scientific paper

10.1007/s11854-011-0003-1

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 $f \colon M \ra M$ such that $f(p) = q$. In this paper, we show there exists a universal constant $\KK > 1$ such that if $M$ is a $K$-quasiconformally homogeneous hyperbolic genus zero surface other than $\D^2$, then $K \geq \KK$. This answers a question by Gehring and Palka.

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