Holomorphic motions, Fatou linearization, and quasiconformal rigidity for parabolic germs

Yunping Jiang
2009 The Michigan mathematical journal  
By applying holomorphic motions, we prove that a parabolic germ is quasiconformal rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller and smaller neighborhoods. Before to prove this theorem, we use the idea of holomorphic motions to give a conceptual proof of the Fatou linearization theorem. As a byproduct, we also prove that any
more » ... te number of analytic germs at different points in the Riemann sphere can be extended to a quasiconformal homeomorphism which can be more and more near conformal as as long as we consider these germs defined on smaller and smaller neighborhoods of these points. 2000 Mathematics Subject Classification. Primary 37F99, Secondary 32H02.
doi:10.1307/mmj/1250169075 fatcat:c4pgodp2z5bq7fsolrf3sry46a