Convex hypersurfaces with prescribed Gauss-Kronecker curvature (Q756727)
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scientific article; zbMATH DE number 4192577
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convex hypersurfaces with prescribed Gauss-Kronecker curvature |
scientific article; zbMATH DE number 4192577 |
Statements
Convex hypersurfaces with prescribed Gauss-Kronecker curvature (English)
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1991
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A curvature flow method is developed in studying the question when a positive function in the Euclidean space is the Gauss-Kronecker curvature for a convex hypersurface. A necessary and sufficient condition for the existence of a minimum which is a solution hypersurface is obtained. Multiple solutions are also found.
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Monge-Ampère equation
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mountain pass method
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curvature flow method
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Gauss-Kronecker curvature
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convex hypersurface
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