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By applying holomorphic motions, we prove that a parabolic germ isquasiconformally rigid, that is, any two topologically conjugate parabolicgerms are quasiconformally conjugate and the conjugacy can be chosen to be moreand more near conformal as long as we consider these germs defined on smallerand smaller neighborhoods. Before proving this theorem, we use the idea ofholomorphic motions to give a conceptual proof of the Fatou linearizationtheorem. As a by-product, we also prove that any finite number of analyticgerms at different points in the Riemann sphere can be extended to aquasiconformal homeomorphism which can be more and more near conformal as aslong as we consider these germs defined on smaller and smaller neighborhoods ofthese points.

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