Length and area estimates for (hyperbolically) convex conformal mappings

DOI10.1007/s40315-018-0254-2zbMath1404.30019OpenAlexW2897294778WikidataQ129161858 ScholiaQ129161858MaRDI QIDQ1634281

Maria Kourou

Publication date: 18 December 2018

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-018-0254-2

zbMATH Keywords

conformal mappingsubharmonic functionsuperharmonic functionhyperbolic lengthhyperbolic areaconvex univalent functionhyperbolically convex mapping

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) General theory of conformal mappings (30C35) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (1)

Geometric versions of Schwarz’s lemma for spherically convex functions

Cites Work

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• Hyperbolic geometry in k-convex regions
• Problems and theorems in analysis. I. Series, integral calculus, theory of functions. Transl. from the German by Dorothee Aeppli
• On hyperbolically convex functions
• Area inequality and \(Q_{p}\) norm
• Characterizations of hyperbolically convex regions
• Geometric versions of Schwarz’s lemma for quasiregular mappings
• Schwarzian derivatives of convex mappings
• Multi-point variations of the Schwarz lemma with diameter and width conditions
• Conformal mapping, convexity and total absolute curvature
• Monotonicity theorems for analytic functions centered at infinity
• Area, capacity and diameter versions of Schwarz’s Lemma
• On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane
• Hyperbolically convex functions II
• Hyperbolically convex functions
• Hyperbolically 1-convex functions
• Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius
• Hyperbolic geometric versions of Schwarz’s lemma
• Some Inequalities for Convex and Star-Shaped Domains

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