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arXiv · 1309.2885

Finitely connected domains, Rational maps and Ahlfors functions

Maxime Fortier Bourque·Malik Younsi
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Abstract

Using Ahlfors functions, Grunsky maps and the Bell representation theorem, we show that a certain subset of the rational maps of degree $n$ forms a trivial bundle over the moduli space of non-degenerate $n$-connected domains with one marked tangent vector with fiber the $n$-fold symmetric product of the circle. A consequence is that the set of rational Ahlfors functions of degree $n$ forms a closed embedded submanifold inside the space of rational maps of degree $n$. As an application, we show the existence of rational Ahlfors functions with non-positive residues, resolving a question left open in a previous paper by the authors.

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Maxime Fortier Bourque, Malik Younsi. 2013-09-11. Finitely connected domains, Rational maps and Ahlfors functions. https://arxiv.org/abs/1309.2885

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