Conjugacies between rational maps and extremal quasiconformal maps

Cui, Guizhen

doi:10.1090/S0002-9939-01-05918-4

Conjugacies between rational maps and extremal quasiconformal maps
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Proc. Amer. Math. Soc. 129 (2001), 1949-1953 Request permission

Abstract:

We show that two rational maps which are $K$-quasiconformally combinatorially equivalent are $K$-quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.

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