Some geometric aspects of the work of Lars Ahlfors (Q2702306)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some geometric aspects of the work of Lars Ahlfors |
scientific article |
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8 January 2002
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Schwarz lemma
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Ahlfors-Schwarz lemma
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conformal metric
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negative curvature
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hyperbolic metric
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Some geometric aspects of the work of Lars Ahlfors (English)
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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].
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