The verification of an inequality
type: Item
instance of: scholarly article
title: The verification of an inequality
zbMATH Open document ID: 1183.30019
author: Roger W. Barnard
author: Kent Pearce
published in: The Journal of Analysis
publication date: 2009-11-18T00:00:00Z
review text: In a recent paper [\textit{R. W. Barnard, L. Cole, K. Pearce} and \textit{G. Brock Williams}, Proc. Lond. Math. Soc. (3) 93, No. 2, 395--417 (2006; Zbl 1103.30012)], the authors verified a conjecture of Mejia and Pommerenke that the extremal value for the Schwarzian derivative of a hyperbolically convex function is realized by a symmetric hyperbolic ``strip'' mapping. In the proof appeared an assertion that ``using an extensive computational argument which considers several cases'', the problem of computing the Schwarzian derivative for hyperbolic polygons bounded by exactly two symmetric hyperbolic geodesics could be reduced to computing the Schwarzian derivative for hyperbolic polygons bounded by exactly two symmetric hyperbolic geodesics, under the assumption that the argument \(z\) of the Schwarzian derivative satisfies the restriction \(0 \leq z < 1\). In the present paper, the authors provide a verification for that assertion.
reviewed by: Agnieszka Wisniowska-Wajnryb
Mathematics Subject Classification ID: 30C70
zbMATH DE Number: 5635037
zbMATH Keywords: hyperbolically convex function
zbMATH Keywords: Schwarzian derivative
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description: scientific article; zbMATH DE number 5635037