On an extension of Liouville's theorem (Q1188370)
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scientific article; zbMATH DE number 40542
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an extension of Liouville's theorem |
scientific article; zbMATH DE number 40542 |
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On an extension of Liouville's theorem (English)
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13 August 1992
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The author proves a Liouville type theorem for mappings \(w\) of the complex plane. Earlier such a result (\(w\) bounded \(\Rightarrow w\) constant) was known for quasiregular maps. Here the author proves a similar result by weakening the assumption that \(w\) be quasiregular to the requirement that \(w\) be quasiregular in \(\{z\in\mathbb{C}\mid| z|<R\}\) with restrictions on the growth of the maximal dilatation as \(R\to\infty\).
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Liouville type theorem
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quasiregular maps
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maximal dilatation
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0.9586564
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