Existence of vertical ends of mean curvature \(1/2\) in \(\mathbb {H}^{2} \times \mathbb {R}\) (Q2880678)
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scientific article; zbMATH DE number 6024124
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of vertical ends of mean curvature \(1/2\) in \(\mathbb {H}^{2} \times \mathbb {R}\) |
scientific article; zbMATH DE number 6024124 |
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13 April 2012
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vertical end of mean curvature \(1/2\)
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\(\mathbb {H}^{2} \times \mathbb {R}\)
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Existence of vertical ends of mean curvature \(1/2\) in \(\mathbb {H}^{2} \times \mathbb {R}\) (English)
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The Perron process is used by the authors to solve a certain Dirichlet problem for the mean curvature equation \(H=\frac{1}{2}\) over some exterior domains in \(\mathbb{H}\times \{0\}\). A main tool in the proof is a Convex Hull Lemma which gives horizontal and vertical distance estimates in many geometrical situations.
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