Applications of hyperbolic convexity to Euclidean and spherical convexity

DOI10.1007/BF02792893zbMath0638.30007OpenAlexW2045889075MaRDI QIDQ1099282

David Minda

Publication date: 1987

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02792893

zbMATH Keywords

hyperbolic metrichyperbolic geodesichyperbolic convexity

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) General theory of conformal mappings (30C35) Geodesics in global differential geometry (53C22)

Related Items (5)

Conformal mapping, convexity and total absolute curvature ⋮ Behavior of domain constants under conformal mappings ⋮ Geometric versions of Schwarz’s lemma for spherically convex functions ⋮ The Bohr inequality in the hyperbolic plane ⋮ Two-point distortion theorems for spherically convex functions

Cites Work

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• Lower bounds for the hyperbolic metric in convex regions
• Spirals and the universal Teichmüller space
• The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in \(| z| < 1\)
• On an inequality for the hyperbolic measure and its applications in the theory of functions
• The hyperbolic metirc and bloch constants for spherically convex regions
• A reflection principle for the hyperbolic metric and applications to geometric function theory
• A Remark on Linear Elliptic Differential Equations of Second Order

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