Existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature

DOI10.1090/S0002-9947-96-01650-9zbMath0926.53024MaRDI QIDQ3837651

Xu-Jia Wang

Publication date: 10 December 1996

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

zbMATH Keywords

convex hypersurfacesGauss curvature flowprescribed curvaturestable and unstable solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Existence and extendibility of rotationally symmetric graphs with a prescribed higher mean curvature function in Euclidean and Minkowski spaces ⋮ A priori estimates and existence of solutions to the prescribed centroaffine curvature problem ⋮ Smooth solutions to the \(L_p\) dual Minkowski problem ⋮ A maximum problem of S.-T. Yau for variational \(p\)-capacity ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ A class of anisotropic expanding curvature flows ⋮ Anisotropic inverse harmonic mean curvature flow ⋮ The dual Minkowski problem for symmetric convex bodies ⋮ Anisotropic Gauss curvature flows and their associated Dual Orlicz-Minkowski problems

Cites Work

• Convex hypersurfaces with prescribed Gauss-Kronecker curvature
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• A logarithmic Gauss curvature flow and the Minkowski problem.
• Infinite dimensional Morse theory and multiple solution problems
• On a real Monge-Ampère functional
• 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
• On the regularity of the solution of then-dimensional Minkowski problem
• Hypersurfaces in IRⁿ⁺¹with prescribed gaussian curvature and related equations of monge—ampére type
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