Distortion theorems for higher order Schwarzian derivatives of univalent functions

DOI10.1090/S0002-9939-00-05623-9zbMath0953.30012OpenAlexW1564741747MaRDI QIDQ4505875

Eric D. Schippers

Publication date: 3 October 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05623-9

zbMATH Keywords

Schwarzian derivativedistortion theoremshyperbolic metricunivalent functionsMöbius transformationSchwarzian derivatives

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)

Related Items (18)

Invariant Schwarzian derivatives of higher order ⋮ Estimate for Schwarzian derivative of certain close-to-convex functions ⋮ Higher Bers maps and BMO-Teichmüller space ⋮ A study of the higher-order Schwarzian derivatives of Hirotaka Tamanoi ⋮ Remarks on higher Schwarzians ⋮ Teichmüller spaces and coefficient problems for univalent holomorphic functions ⋮ Unnamed Item ⋮ Morrey type Teichmüller space and higher Bers maps ⋮ A Shimorin-type estimate for higher-order Schwarzian derivatives ⋮ Geometric invariants associated with projective structures and univalence criteria ⋮ Teichmüller spaces and coefficient problems for univalent holomorphic functions ⋮ Schwarzian derivative, integral means, and the affine and linear invariant families of biharmonic mappings ⋮ The universal Teichmüller space and function space ⋮ Generalized Schwarzian derivatives and higher order differential equations ⋮ Conformal invariants and higher-order Schwarz lemmas ⋮ Sharp bounds on the higher order Schwarzian derivatives for Janowski classes ⋮ Taylor coefficients of negative powers of schlicht functions ⋮ Higher Schwarzian derivative and Dirichlet Morrey space

Cites Work

• Unnamed Item
• Unnamed Item
• Two-point distortion theorems for univalent functions
• Coefficient estimates for negative powers of the derivative of univalent functions
• Aharonov invariants and univalent functions
• Higher Schwarzian operators and combinatorics of the Schwarzian derivative
• On \(m\)-\(m\) disconjugacy of differential equations
• The Schwarzian derivative and schlicht functions

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