Hyperbolically Convex Functions

  • Diego Mejía
  • Christian Pommerenke
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 10)

Abstract

A conformal map f of the unit disk D of the complex plane into itself is called hyperbolically convex if the hyperbolic segment between any two points of f (D) also lies in f (D). These functions form a non-linear space invariant under Moebius transformations of D onto itself. The fact that this space is non-linear makes it impossible to use many of the standard methods.

This survey talk will concentrate on
  • Analytic characterizations of h-convex functions

  • Inequalities for h-convex functions

  • Hausdorff dimension of image sets

A few proofs will be sketched.

Keywords

Hausdorff Dimension Fuchsian Group Hyperbolic Geometry Analytic Characterization Jordan Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Diego Mejía
    • 1
  • Christian Pommerenke
    • 2
  1. 1.Departamento de MatemáticasUniversidad NacionalMedellínColombia
  2. 2.Fachbereich Mathematik, 8-2Technische UniversitätBerlinGermany

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