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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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv42n2a05,
AUTHOR = {Mejía, Diego and Pommerenke, Christian},
TITLE = {{On groups and normal polymorphic functions}},
JOURNAL = {Revista Colombiana de Matemáticas}, ]]>
YEAR = {2008},
volume = {42},
number = {2},
pages = {167-181}
}