Conformal Mapping of Abstract Riemann Surfaces |
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A₂ admissible function arc which separates bdyG bdyH bdyK bdyKm Cauchy-Riemann equations circle with center circular covering class c(1 clockwise component conformal mapping continuous boundary values converges counterclockwise directed d₁ d₂ Definition denotes the set Dirichlet integral Dirichlet principle dx dy element exists a neighborhood exists a positive exists a region f is one-to-one function almost class G₁ G₂ Green's formula H₁ harmonic on G Hausdorff space Hence homeomorphism Hurwitz-Courant interior intersects G K₁ Lemma Let f Let G limit point line integral local uniformizer manifold minimizing sequence open arc ordered triple pairwise disjoint perfectly separable Riemann plane point of G pole of order positive integer Proof provided there exists quasi-simple Radó real numbers real-valued function defined region G S₁ separable Riemann surface separation axiom simple closed curve slit region Stoilow Theorem topological triangulable uniformizer g unit circle v<d₂