Nonpositively curved surfaces in \(\mathbb R^ 3\). (Q1609818)
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scientific article; zbMATH DE number 1782683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonpositively curved surfaces in \(\mathbb R^ 3\). |
scientific article; zbMATH DE number 1782683 |
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Nonpositively curved surfaces in \(\mathbb R^ 3\). (English)
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15 August 2002
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Let \(M\) be a \(C^2\)-regular surface immersed in \(\mathbb R^3\), which consists of one embedded connected component outside a compact set. The authors prove that if \(M\) has non-positive Gaussian curvature and a square integrable second fundamental form, then \(M\) lies between two parallel planes of \(\mathbb R^3\).
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nonpositive curved surface
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square integrable
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