Abstract

MEJIA, DIEGO  and  POMMERENKE, CHRISTIAN. On groups and normal polymorphic functions. Rev.colomb.mat. [online]. 2008, vol.42, n.2, pp.167-181. ISSN 0034-7426.

Let Γ be a Fuchsian group acting on the unit disk D. A function f meromorphic in D is polymorphic if there exists a homomorphism f_* of Γ onto a group Σ of Möbius transformations such that f•γ=f_∗(γ)• f for γ∈Γ. A function is normal if sup(1-|z|²)|f^′(z)|/(1+|f(z)|²)<∞. First we study the behavior of a normal polymorphic function at the fixed points of Γ and then the existence of such functions for a given type of group Σ.

Keywords : Kleinian group; polymorphic function; normalfunction; projective structure.

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