On the regularity of the solution of the n‐dimensional Minkowski problem

Keywords

Minkowski space, Citation, Mathematics, Combinatorics, Operations research

References

• Nonlinear Functional AnalysisJacob T. Schwartz — 1969
• On the regularity of the monge‐ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)Shiu‐Yuen Cheng, Shing–Tung Yau — 1977
• The Weyl and Minkowski problems in differential geometry in the largeLouis Nirenberg — 1953
• Theorie der Konvexen KörperT. Bonnesen, Werner Fenchel — 1934
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens.Eugenio Calabi — 1958

Cited by

• Spacelike hypersurfaces with constant Gauss-Kronecker curvature in the Minkowski spaceAn-Min Li — 1995
• On the regularity of the Lp Minkowski problemYong Huang, Qiuping Lu — 2013
• Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.Udo Simon, Vladimir Oliker — 1983
• Centro-affine normal flows and their applicationsMohammad N. Ivaki — 2012
• Shing-Tung Yau氏の業績小林 昭七 — 1983
• Isometric Embedding of Riemannian Manifolds in Euclidean SpacesQing Han, Jiaxing Hong — 2006
• Régularité Gevrey des solutions de l'équation de Monge-Ampère réelleSaoussen Kallel-Jallouli — 1991
• The planar Orlicz Minkowski problem in the L1-senseSun Yijing, Long Yiming — 2015
• The Dirichlet problem for Monge-Ampère equations in non-convex domains and spacelike hypersurfaces of constant Gauss curvatureBo Guan — 1998
• Construction of Shapes Arising from the Minkowski Problem Using a Level Set ApproachLi‐Tien Cheng — 2003
• Isometric embedding inR3 of complete noncompact nonnegatively curved surfacesHong Jiaxing — 1997
• Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes Application to the Minkowski problem in the Minkowski spaceThierry Barbot, François Béguin, Abdelghani Zeghib — 2008
• The Weyl problem with nonnegative Gauss curvaturePengfei Guan, Yan Yan Li — 1994
• On the _-Minkowski problemErwin Lutwak, Deane Yang, Gaoyong Zhang — 2003
• Convex hypersurfaces with prescribed Gauss-Kronecker curvatureKaising Tso — 1991
• Stability of the Blaschke–Santaló inequality in the planeMohammad N. Ivaki — 2014
• On the regularity of solutions to a generalization of the Minkowski problemErwin Lutwak, Vladimir Oliker — 1995
• The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problemErwin Lutwak — 1993
• EXISTENCE OF CONVEX HYPERSURFACES WITH PRESCRIBED GAUSS-KRONECKER CURVATUREXu‐Jia Wang — 1996
• Limits of Solutions to a Parabolic Monge-Ampere EquationJohn Loftin, Mao‐Pei Tsui — 2008

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