Ahlfors functions on compact bordered Riemann surfaces. (English) Zbl 0981.30021

Author’s abstract: Let \(R\) be a compact bordered Riemann surface which is non-planar. We solve a conjecture posed by Gouma concerning the distribution of degrees of Ahlfors functions on \(R\) whose double is hyperelliptic. Besides we consider the problem when a linear transformation of an Ahlfors function on \(R\) is again an Ahlfors function. We give a necessary and sufficient condition for this problem when the degree of the Ahlfors function is maximal.


30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30F30 Differentials on Riemann surfaces
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