A Unified Approach to Univalence Criteria in the Unit Disc

DOI10.2307/2160900zbMath0811.30013OpenAlexW4238661884MaRDI QIDQ4318426

Martin Chuaqui Farrú

Publication date: 1 May 1995

Full work available at URL: https://doi.org/10.2307/2160900

zbMATH Keywords

Schwarzian derivativeconformal metricunivalence criteriasimply-connected

Mathematics Subject Classification ID

Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (7)

Injectivity of minimal immersions and homeomorphic extensions to space ⋮ An extension of a theorem of Gehring and Pommerenke ⋮ Conformal radius: at the interface of traditions ⋮ John domains and a univalence criterion of Ahlfors ⋮ Bifurcations and new uniqueness criteria for critical points of hyperbolic derivatives ⋮ Ricci Curvature and a Criterion for Simple-Connectivity on the Sphere ⋮ Quasiconformal extensions of harmonic mappings

Cites Work

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• A generalization of Nehari's univalence criterion
• The sub-mean-value property of subharmonic functions and its application to the estimation of the Gaussian curvature of the span metric
• The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions
• The Schwarzian derivative and conformal mapping of Riemannian manifolds
• Univalence criteria depending on the Schwarzian derivative
• Univalence Criteria and Quasiconformal Extensions
• The Schwarzian derivative for conformal maps.
• The hyperbolic Gauss map and quasiconformal reflections.
• The Schwarzian derivative and quasiconformal reflections on S^n
• Sharp Distortion Theorems Associated with the Schwarzian Derivative
• Ricci Curvature and a Criterion for Simple-Connectivity on the Sphere
• The Schwarzian derivative and schlicht functions

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