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On groups and normal polymorphic functions
Sobre grupos y funciones polimorfas normales
Palabras clave:
Kleinian group, polymorphic function, normal function, projective structure (en)Grupo kleiniano, función polimorfa, función normal, estructura proyectiva, 2000 Mathematics Subject Classification. 30F35, 30D45, 30F40 (es)
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Abstract. 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 o ꭚ = f * (ꭚ) o f for ꭚ ∊ Γ. A function is normal if sup (1 - |z|2) | f '(z) |/ (1 + | f (z)|2) < ∞. First we study the behaviour 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.
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 o ꭚ = f * (ꭚ) o f for ꭚ ∊ 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.
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