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Upper estimates for hyperbolic metrics on subdomains
A result concerning upper estimates for hyperbolic metrics on subdomains is proved. The method of proof involves a standard technique based on the...
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On a Multi-Point Schwarz-Pick Lemma
We consider the multi-point Schwarz-Pick Lemma and its associate functions due to Beardon-Minda and Baribeau-Rivard-Wegert. Basic properties of the...
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Conformal Images and the Angle of Parallelism
We use classical hyperbolic geometry to estimate the Euclidean size of the image of a subset of a simply connected hyperbolic region under a...
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On the Geometry of the Quaternionic Unit Disc
In the space ℍ of quaternions, the natural invariant geometry of the open unit disc ΔH, diffeomorphic to the open half-space H+ via a Cayleytype...
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Some Applications of Higher-Order Hyperbolic Derivatives
The notion of higher-order hyperbolic derivatives was recently introduced. As the given definition does not lend to simple calculations, we first...
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A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic Function Theory
In this paper we study a mean-value property for solutions of the Laplace-Beltrami equation Equation 1...
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Erlangen Program at Large: An Overview
This is an overview of the Erlangen Program at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far...
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The Diameter of a Hyperbolic Disc
Recently, Matti Vuorinen asked whether the set-theoretic diameter of a hyperbolic disc of radius r in a hyperbolic plane region Ω is 2 r . The answer...
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Invariant Schwarzian Derivatives of Higher Order
We derive relations between the Aharonov invariants and Tamanoi’s Schwarzian derivatives of higher order and give a recursive formula for Tamanoi’s...
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The Quasiconvexity of Quasigeodesics in Real Normed Vector Spaces
In this paper, we assume that E is a real normed space of dimension at least two. The aim of this paper is to show that, for any convex domain in E ,...
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Uniformly Separated Sets and Gromov Hyperbolicity of Domains with the Quasihyperbolic Metric
In this article we prove comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic metric. By a comparative...
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Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral
We describe, in terms of generalized elliptic integrals, the hyperbolic metric of the twice-punctured sphere with one conical singularity of...
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A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials
In this paper, we define a conformally invariant (pseudo-)metric on all Riemann surfaces in terms of integrable holomorphic quadratic differentials...
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On Hyperbolic Divided Differences and the Nevanlinna-Pick Problem
Starting from the notion of the complex pseudo-hyperbolic distance and the hyperbolic difference quotient introduced by A. F. Beardon and D. Minda in...
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Hypergeometric Functions and Hyperbolic Metric
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the...
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Dieudonné Points of Holomorphic Self-Maps of Regions
Schwarz’s Lemma says that if a holomorphic self-map f of the unit disc fixes the origin then ¦ f ′(0)¦ ≤ 1. In 1931, Dieudonné extended this by showing...
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Minimal length of two intersecting simple closed geodesics
On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we address the question of a sharp lower bound L ...