Surface in \(R^ 3\) with prescribed Gauss curvature (Q1098111)
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scientific article; zbMATH DE number 4036611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Surface in \(R^ 3\) with prescribed Gauss curvature |
scientific article; zbMATH DE number 4036611 |
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Surface in \(R^ 3\) with prescribed Gauss curvature (English)
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1987
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The author proves that for every smooth function K(x,y) which vanishes on a simple closed smooth curve \(\Lambda\) and which satisfies \(dK|_{\Lambda}\neq 0\) there always exists a smooth surface \(z=z(x,y)\) defined in a neighbourhood of \(\Lambda\) with Gaussian curvature K(x,y).
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prescribed curvature
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Gaussian curvature
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