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Solution of the Dirichlet Problem for a Schlicht Region
Function Theoretic Majorant Principles
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according Ahlfors analytic function assume asymptotic values boundary arcs boundary point boundary values bounded type branch points characteristic T(r circle closed point set co(z conformal mapping connected region consequently consider convergent corresponding counting function cross cuts deficiency defined exceptional values finite number follows formula function w(z given Green's function harmonic function harmonic measure harmonic measure zero hence hyperbolic inequality infinite infinity integral interior point interval Jordan arcs lemma length limit line complex logarithmic mapping function maximum principle mean sheet number measure zero meromorphic function metric monotonically Nevanlinna nonnegative null set obtain one-to-one parabolic Picard's theorem poles polygons proof properties quantity ramification region G relation result Riemann surface Robin constant schlicht region second main theorem sequence simply connected single-valued subregion subset surface F topological unit disk universal covering surface upper bound vanishes w-plane