Precise Bounds in the Theorems of Schottky and Picard

DOI10.1112/jlms/s2-21.2.279zbMath0431.30017OpenAlexW2029561997MaRDI QIDQ3868042

Joachim A. Hempel

Publication date: 1980

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/jlms/s2-21.2.279

zbMATH Keywords

elliptic modular functionhyperbolic metricmeromorphic functionsessential singularitytheorems of Schottky and Picard

Mathematics Subject Classification ID

Meromorphic functions of one complex variable (general theory) (30D30)

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Hypergeometric functions and hyperbolic metric ⋮ Construction of nearly hyperbolic distance on punctured spheres ⋮ Agard's \(\eta\)-distortion function and Schottky's theorem ⋮ Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky ⋮ On Gol'dberg's constant \(A_2\) ⋮ Schottky-Landau growth estimates for \(s\)-normal families of holomorphic mappings ⋮ Estimates for the hyperbolic metric of the punctured plane and applications ⋮ Modular equations and distortion functions ⋮ Topics in special functions. II ⋮ Sharp lower bounds for the hyperbolic metric of the complement of a closed subset of the unit circle and theorems of Schwarz-Pick-, Schottky- and Landau-type for analytic functions ⋮ A remark on Schottky's theorem ⋮ Singular values, quasiconformal maps and the Schottky upper bound ⋮ The Distortion Theorem for quasiconformal mappings, Schottky’s Theorem and holomorphic motions ⋮ Some inequalities for the Poincaré metric of plane domains

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