Hyperbolically Convex Functions
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.
Analytic characterizations of h-convex functions
Inequalities for h-convex functions
Hausdorff dimension of image sets
KeywordsHausdorff Dimension Fuchsian Group Hyperbolic Geometry Analytic Characterization Jordan Domain
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