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