Conformal Mapping of Abstract Riemann Surfaces |
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analytic assigned bdyG bdyH bdyK bdyKm boundary bounded called chapter Choose circular covering circular region class c(1 collection compact component conclusion conformal cover conformal mapping connected consider constant continuous converges counterclockwise directed d₁ d₂ Definition denotes the set derivative dx dy element end-point exists a point exists a region f maps finite follows function almost class G₁ G₂ Hausdorff space Hence homeomorphism interior intersects K₁ Lemma Let G limit point manifold maps G minimizing sequence neighborhood one-to-one open arc ordered triple orientation origin perfectly separable Riemann plane point of G positive integer possesses preferred Proof properties proved provided there exists quasi-simple real-valued function region containing region G regular relative separable Riemann surface simple closed curve sphere Stoilow subset symbol Theorem topological triangulable uniformizer uniformly values vanishes zero