New elementary proofs establish complete Kobayashi hyperbolicity for the twice-punctured plane and bounded planar domains without using the disk cover or negative curvature, with applications to Picard-type theorems and a Hahn-inspired characterization.
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A proof of the uniformization theorem for domains in the Riemann sphere is given via the Kobayashi metric without relying on the elliptic modular function.
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Revisiting Kobayashi hyperbolicity on planar domains
New elementary proofs establish complete Kobayashi hyperbolicity for the twice-punctured plane and bounded planar domains without using the disk cover or negative curvature, with applications to Picard-type theorems and a Hahn-inspired characterization.
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Uniformization of domains in the Riemann sphere via the Kobayashi metric
A proof of the uniformization theorem for domains in the Riemann sphere is given via the Kobayashi metric without relying on the elliptic modular function.