A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature

DOI10.1007/BF02570839zbMath0735.53048MaRDI QIDQ811518

Kai-Seng Chou

Publication date: 1992

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174368

zbMATH Keywords

convex hypersurfacesGauss-Kronecker curvatureMonge-Ampère equationsAleksandrov's formula

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

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A maximum problem of S.-T. Yau for variational \(p\)-capacity ⋮ Flux \& radii within the subconformal capacity ⋮ Geometrical logarithmic capacitance

Cites Work

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• Convex hypersurfaces with prescribed Gauss-Kronecker curvature
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Regularity of generalized solutions of Monge-Ampère equations
• Curvature Measures
• The Problem of Embedding S n Into R n+1 With Prescribed Gauss Curvature and Its Solution by Variational Methods
• Plongements radiaux $S\sp n\hookrightarrow {R}\sp {n+1}$ à courbure de Gauss positive prescrite
• Hypersurfaces in IRⁿ⁺¹with prescribed gaussian curvature and related equations of monge—ampére type

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