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Analytic functions in a lacunary end of a Riemann surface

Zenjiro Kuramochi (1975)

Annales de l'institut Fourier

Let G be an end of a Riemann surface with null boundary and let G ' be a lacunary end with a closed set F = G - G ' . We study minimal functions in G and G ' to show that G and G ' have similar properties if F is thinly distributed on the ideal boundary. We discuss the behaviour of analytic functions in G ' and relation between the existence of analytic functions of some classes in G ' and the structure of Martin’s boundary points over the end G . Also we show that the existence of complicated Martin’s boundary points...

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