The Problem of Embedding S n Into R n+1 With Prescribed Gauss Curvature and Its Solution by Variational Methods

DOI10.2307/2000157zbMath0589.49028OpenAlexW4240948490MaRDI QIDQ3717712

Vladimir I. Oliker

Publication date: 1986

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2000157

zbMATH Keywords

variational calculusclosed convex hypersurfacesprescribed Gauss curvaturenonlinear elliptic differential equation of Monge-Ampère type

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (4)

A maximum problem of S.-T. Yau for variational \(p\)-capacity ⋮ Deforming convex hypersurfaces to a hypersurface with prescribed harmonic mean curvature ⋮ Existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature ⋮ A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature

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