¹Universidad Nacional de Colombia, Medellín, Colombia. Email: dmejia@unal.edu.co
²Universidad Nacional de Colombia, Medellín, Colombia. Email: pommeren@math.tu-berlin.de

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.

Key words: Kleinian group, polymorphic function, normalfunction, projective structure.

Sea Γ un grupo fuchsiano que actúa en el disco unitario D. Una función f meromorfa en D es polimorfa si existe un homomorfismo f_∗ de Γ sobre un grupo Σ de transformaciones de Möbius tal que f•γ=f_∗(γ)• f para γ∈Γ. Una función es normal si sup(1-|z|²)|f^′(z)|/(1+|f(z)|²)<∞. Primero estudiamos el comportamiento de una función polimorfa normal en los puntos fijos de Γ y después la existencia de tales funciones para un tipo de grupo Σ dado.

Palabras clave: Grupo kleiniano, función polimorfa, función normal, estructura proyectiva.

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