A non-existence result for harmonic mappings from \(R^ n\) into \(H^ n\) (Q1262590)
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scientific article; zbMATH DE number 4124645
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-existence result for harmonic mappings from \(R^ n\) into \(H^ n\) |
scientific article; zbMATH DE number 4124645 |
Statements
A non-existence result for harmonic mappings from \(R^ n\) into \(H^ n\) (English)
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1988
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It is shown that there exists no harmonic map from the whole Euclidean space \(R^ n\) into a real hyperbolic n-space \(H^ n\) whose coordinate representation u(x) with respect to the normal coordinate system satisfies the inequality \(| D(u/| u|)|^ 2\geq (n- 1)/| x|^ 2\).
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Riemannian manifold
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Laplace-Beltrami operator
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harmonic map
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