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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1999; 36(6): 1169-1180

Printed November 1, 1999

Copyright © The Korean Mathematical Society.

A geometric approach to two-point comparisons for hyperbolic and Euclidean geometry

Seong-A Kim and David Minda

Abstract

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Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane $\C$ are known (\cite{KM2}, \cite{MM1}). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

Keywords: the hyperbolic metric, convex region

MSC numbers: 30C45

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