A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature (Q811518)
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scientific article; zbMATH DE number 4215951
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature |
scientific article; zbMATH DE number 4215951 |
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A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature (English)
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1992
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The question about when a positive function defined in \(\mathbb{R}^ n\) is the Gauss-Kronecker curvature of a closed hypersurface is studied by means of the direct method in the calculus of variations. A necessary and sufficient condition for the existence of a minimizer for the corresponding functional is obtained.
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Gauss-Kronecker curvature
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convex hypersurfaces
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Monge-Ampère equations
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Aleksandrov's formula
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