Some geometric aspects of the work of Lars Ahlfors
type: Item
instance of: scholarly article
zbMATH Open document ID: 0977.30001
author: Robert Brooks
publication date: 2002-01-08T00:00:00Z
Mathematics Subject Classification ID: 30-03
Mathematics Subject Classification ID: 01A70
Mathematics Subject Classification ID: 30F45
zbMATH DE Number: 1574733
zbMATH Keywords: Schwarz lemma
zbMATH Keywords: Ahlfors-Schwarz lemma
zbMATH Keywords: conformal metric
zbMATH Keywords: negative curvature
zbMATH Keywords: hyperbolic metric
MaRDI profile type: Publication
title: Some geometric aspects of the work of Lars Ahlfors
review text: In this survey article the author reviews Ahlfors' formulation of the classical Schwarz lemma in terms of conformal metrics of negative curvature and distance decreasing mappings. The paper also presents an application of \textit{S. Wolpert}'s version of the Ahlfors-Schwarz lemma [Proc. Am. Math. Soc. 84, 377-378 (1982; Zbl 0483.30027)] to study the hyperbolic metric near punctures [\textit{R. Brooks}, Comment. Math. Helv. 74, No. 1, 156-170 (1999; Zbl 0920.30027)]. The author finally presents Ahlfors' use of ultrahyperbolic metrics to obtain a lower bound for the Bloch constant.NEWLINENEWLINEFor the entire collection see [Zbl 0944.00101].
reviewed by: Martin Chuaqui
description: scientific article