On a J. C. C. Nitsche's type inequality for the hyperbolic space \(\mathbf H^3\) (Q462319)
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scientific article; zbMATH DE number 6358459
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a J. C. C. Nitsche's type inequality for the hyperbolic space \(\mathbf H^3\) |
scientific article; zbMATH DE number 6358459 |
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On a J. C. C. Nitsche's type inequality for the hyperbolic space \(\mathbf H^3\) (English)
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20 October 2014
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The article considers the three-dimensional hyperbolic space \(\mathbb{H}^3\) in the Poincaré disc model with the Poincaré metric \(d_h\). Let \(\mathcal A(x_0,p,q):=\{x:p<d_h(x,x_0)<q\}\subset\mathbb{H}^3\) be a hyperbolic annulus with the inner and outer radii \(0<p<q<\infty\). The article characterizes hyperbolic harmonic diffeomorphisms between two annuli. Moreover, radial harmonic mappings between two given annuli satisfying certain conditions are constructed.
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harmonic mappings
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spherical annuli
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hyperbolic geometry
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Nitsche bound
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