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Convex hypersurfaces of prescribed curvatures. (English) Zbl 1025.53028

The authors consider the problem of finding closed strictly convex hypersurfaces in \(\mathbb R^{n+1}\) whose Weingarten curvatures are prescribed as a function defined on \(S^n\) in terms of the inverse Gauss map.

MSC:

53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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