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On Riemann Surfaces, on which no Bounded 4 Harmonic Function Exists

On Riemann Surfaces, on which no Bounded 4 Harmonic Function Exists

Let $F$ be a Riemann surface spread over the z-plane, on which $no$ one-valued, bounded and non-constant harmonic function exists.If' $F$ possesses no Green's function, the above condition is satisfied as Myrberg provedl).