an:05995330
Zbl 1239.30007
Bonfert-Taylor, Petra; Martin, Gaven; Reid, Alan W.; Taylor, Edward C.
Teichm??ller mappings, quasiconformal homogeneity, and non-amenable covers of Riemann surfaces
EN
Pure Appl. Math. Q. 7, No. 2, 455-468 (2011).
00284123
2011
j
30C65 30F60
quasiconformal homogeneity; Riemann surface; hyperbolic orbifold
Summary: We show that there exists a universal constant \(K_c\) so that every
\(K\)-strongly quasiconformally homogeneous hyperbolic surface \(X\) (not equal to
\(\mathbb{H}^2\)) has the property that \(K> K_c > 1\). The constant \(K_c\) is the best possible,
and is computed in terms of the diameter of the \((2, 3, 7)\)-hyperbolic orbifold
(which is the hyperbolic orbifold of smallest area). We further show that
the minimum strong homogeneity constant of a hyperbolic surface without
conformal automorphisms decreases if one passes to a non-amenable regular
cover.