Non-simply connected minimal planar domains in \(\mathbb H^2\times\mathbb R\) (Q2855923)
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scientific article; zbMATH DE number 6218179
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-simply connected minimal planar domains in \(\mathbb H^2\times\mathbb R\) |
scientific article; zbMATH DE number 6218179 |
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23 October 2013
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minimal surfaces
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minimally embedded planar domains
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Jenkins-Serrin graphs
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Non-simply connected minimal planar domains in \(\mathbb H^2\times\mathbb R\) (English)
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The main result of this paper shows that for any non-simply connected planar domain there exists a proper minimal embedding of that domain into \(\mathbb H^2\times\mathbb R\). The embedding the authors construct is such that its image has parabolic type and is a vertical bi-graph symmetric with respect to a horizontal slice. The authors' work is based on methods that rely on results obtained by \textit{H. Jenkins} and \textit{J. Serrin} [Bull. Am. Math. Soc. 72, 102--106 (1966; Zbl 0134.08502)] for the Dirichlet problem for minimal graphs with infinite data.
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