AMBIENT QUASICONFORMAL HOMOGENEITY OF PLANAR DOMAINS

作者：Bonfert Taylor Petra^*; Canary Richard D; Martin Gaven; Taylor Edward C; Wolf Michael

来源：Annales Academiae Scientiarum Fennicae-Mathematica, 2010, 35(1): 275-283.

• Quasiconformal homogeneity
• hyperbolic planar domain
• Kleinian groups
• quasiconformal removability

We prove that the ambient quasiconformal homogeneity constant of a hyperbolic planar domain which is not simply connected is uniformly bounded away from 1.
We also consider a component Do of the domain of discontinuity of a finitely generated Kleinian group Gamma. We show that if Omega(0)/Gamma is compact, then Do is uniformly ambiently quasiconformally homogeneous, and that if Do is not simply connected and its quotient Omega(0)/Gamma is non-compact, then Do is not uniformly quasiconformally homogeneous.

• 出版日期2010