Complete space-like surfaces with constant mean curvature in the Minkowski 3-space (Q1122798)
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scientific article; zbMATH DE number 4107644
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complete space-like surfaces with constant mean curvature in the Minkowski 3-space |
scientific article; zbMATH DE number 4107644 |
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Complete space-like surfaces with constant mean curvature in the Minkowski 3-space (English)
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1988
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The author uses the maximum principle to prove the following theorem: The hyperbolic cylinder is the only complete spacelike surface in Minkowski 3-space with non-zero constant mean curvature whose principal curvatures \(k_ 1\) and \(k_ 2\) satisfy \((k_ 1-k_ 2)^ 2\geq \epsilon\) for some positive number \(\epsilon\). The first proof of this theorem has been given by \textit{T. K. Milnor} [Trans. Am. Math. Soc. 280, 161-185 (1983; Zbl 0532.53047)] using different methods.
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maximum principle
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hyperbolic cylinder
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complete spacelike surface
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constant mean curvature
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0.8764346837997437
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0.8347817063331604
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0.8327297568321228
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0.8265864849090576
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