an:05177885
Zbl 1133.30012
Bonfert-Taylor, Petra; Bridgeman, Martin; Canary, Richard D.; Taylor, Edward C.
Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms
EN
Math. Proc. Camb. Philos. Soc. 143, No. 1, 71-84 (2007).
00210196
2007
j
30F45
\(K\)-quasiconformally homogeneous manifold; uniformly quasiconformally homogeneous manifold; Kleinian group; quasiconformal homogeneity constant; moduli space
The main result is the following
Theorem. For each \(c\in (0,2]\), there exists \(K_c> 1\), such that if \(S\) is a \(K\)-quasiconformal homogeneous closed hyperbolic surface of genus \(g\) that admits a non-trivial conformal automorphism with at least \(c(g+ 1)\) fixed points, then \(K\geq K_c\).
The authors consider the strongly (extremely) \(K\)-quasiconformally homogeneous hyperbolic surface as a surface \(S\), such that for any \(x,y\in S\), there is a \(K\)-quasiconformal homeomorphism of taking \(x\) to \(y\), which is homotopic to a conformal automorphism (identity) of \(S\).
In these cases, one can bound the associated quasiconformal homogeneity constant uniformly away from 1.
A. Neagu (Ia??i)