Linear Weingarten surfaces in \(\mathbb R^3\) (Q1871770)
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scientific article; zbMATH DE number 1903795
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear Weingarten surfaces in \(\mathbb R^3\) |
scientific article; zbMATH DE number 1903795 |
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Linear Weingarten surfaces in \(\mathbb R^3\) (English)
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4 May 2003
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Properties of linear Weingarten immersions are studied. Using the conformal structure, two partial differential equations are obtained in the case of linear elliptic Weingarten surfaces. This recovers the possibility to derive the immersion from a harmonic local diffeomorphism into the unit sphere. It was also extended the results of Rosenberg-Earp in giving the optimal estimates of the height that a compact elliptic linear Weingarten surface can arise above the plane.
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Weingarten surface
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height area
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constant mean curvature
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constant Gauss curvature
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