Schwarzian derivatives, the Poincaré metric and the kernel function

DOI10.1007/BF02566674zbMath0438.30014OpenAlexW2013418461MaRDI QIDQ1141784

Frederick W. Gehring, Alan F. Beardon

Publication date: 1980

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/139813

zbMATH Keywords

Schwarzian derivativekernel functionunivalentBergman functionPoincare metric

Mathematics Subject Classification ID

Extremal problems for conformal and quasiconformal mappings, other methods (30C75) General theory of univalent and multivalent functions of one complex variable (30C55) Kernel functions in one complex variable and applications (30C40)

Related Items (18)

Grunsky inequalities and Fredholm spectrum in general domains ⋮ Boundary behaviors of the Poincaré density and its derivatives near a nonisolated boundary point ⋮ Geodesic excursions to infinity in Riemann surfaces ⋮ The Harnack and other conformally invariant metrics ⋮ Behavior of domain constants under conformal mappings ⋮ Univalence Criteria in Multiply-Connected Domains ⋮ On Sets of Mutually Disjoint Univalent Meromorphic Functions ⋮ Extremal problems of Bloch function spaces ⋮ Invariant Operators and Univalent Functions ⋮ Sufficient conditions for the finite-valence of analytic functions and their applications ⋮ Spirals and the asymptotic Teichmüller space ⋮ Distortion control of conjugacies between quadratic polynomials ⋮ Criteria for univalence and quasiconformal extension for harmonic mappings on planar domains ⋮ On the Schwarz derivative, the Bloch space and the Dirichlet space ⋮ The Area of the Complement of a Conformally Rigid Domain ⋮ On the Koebe and Bieberbach constants for a hyperbolic planar domain ⋮ Bergman kernel function and univalence criteria ⋮ Univalent analytic functions and the Poincaré metric

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