Sphere-preserving maps in inversive geometry (Q2781244)
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scientific article; zbMATH DE number 1720991
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sphere-preserving maps in inversive geometry |
scientific article; zbMATH DE number 1720991 |
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Sphere-preserving maps in inversive geometry (English)
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19 March 2002
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Möbius transformation
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conformal map
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sphere preserving map
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cross-ratio
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circle preserving map
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In this paper, the authors study sphere-preserving maps defined on subdomains of the Euclidean space of any dimension \(n\). They give results in this setting that follow from local, rather than global, conditions. They discuss the relationship of sphere-preserving maps to Möbius maps and to maps that preserve cross-ratios. In the special case \(n=2\), the authors relate the ideas discussed here to the solutions of certain functional equations.
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