UNIFORMLY QUASIREGULAR SEMIGROUPS IN TWO DIMENSIONS

摘要: Let G be a semigroup of K-quasiregular or K-quasimeromorphic functions map- ping given open set U in the Riemann sphere into itself, for fixed K, operation being composition functions. We prove that if satisfies an algebraic condition, which is true all abelian semigroups, then there exists K-quasiconformal homeomorphism onto V such f ◦G◦f −1 are meromorphic itself. In particular, whole elements ◦G ◦f rational give example generated by two on sphere, each quasiconformally conjugate to quadratic polynomial, cannot conjugated another homeo- morphisms. These results extend and complement similar positive conjugacy result Tukia Sullivan groups homeomorphisms.