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- Minkowski_problem abstract "In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface S whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly positive real function ƒ defined on a sphere, and the surface that is to be constructed should have Gaussian curvature ƒ(n(x)) at the point x, where n(x) denotes the normal to S at x. Eugenio Calabi stated: "From the geometric view point it [the Minkowski problem] is the Rosetta Stone, from which several related problems can be solved."The problem of radiolocation is easily reduced to the Minkowski problem in Euclidean 3-space: restoration of convex shape over the given Gauss surface curvature. The inverse problem of the short-wave diffraction is reduced to the Minkowski problem. The Minkowski problem is the basis of the mathematical theory of diffraction as well as for the physical theory of diffraction. In the 1960s Petr Ufimtsev (P. Ya. Ufimtsev) began developing a high-frequency asymptotic theory for predicting the scattering of electromagnetic waves from two-dimensional and three-dimensional objects. Now this theory is well known as the physical theory of diffraction (PTD). This theory played the main role in the design of American stealth-aircraft F-117 and B-2.In 1953 Louis Nirenberg published the solutions of two long standing open problems, the Weyl problem and the Minkowski problem in Euclidean 3-space. L. Nirenberg's solution of the Minkowski problem was a milestone in global geometry. He has been selected to be the first recipient of the Chern Medal (in 2010) for his role in the formulation of the modern theory of non-liner elliptic partial differential equations, particularly for solving the Weyl problem and the Minkowski problems in Euclidean 3-space.A. V. Pogorelov received Ukraine State Prize (1973) for resolving the multidimensional Minkowski problem in Euclidean spaces. Pogorelov resolved the Weyl problem in Riemannian space in 1969.Shing-Tung Yau's joint work with S. Y. Cheng gives a complete proof of the higher-dimensional Minkowski problem in Euclidean spaces. Shing-Tung Yau received the Fields Medal at the International Congress of Mathematicians in Warsaw in 1982 for his work in global differential geometry and elliptic partial differential equations, particularly for solving such difficult problems as the Calabi conjecture of 1954, and a problem of Hermann Minkowski in Euclidean spaces concerning the Dirichlet problem for the real Monge–Ampère equation.".
- Minkowski_problem wikiPageID "27966551".
- Minkowski_problem wikiPageLength "4915".
- Minkowski_problem wikiPageOutDegree "31".
- Minkowski_problem wikiPageRevisionID "674550608".
- Minkowski_problem wikiPageWikiLink Aleksei_Pogorelov.
- Minkowski_problem wikiPageWikiLink Calabi_conjecture.
- Minkowski_problem wikiPageWikiLink Category:Differential_geometry.
- Minkowski_problem wikiPageWikiLink Category:Partial_differential_equations.
- Minkowski_problem wikiPageWikiLink Category:Theorems_in_geometry.
- Minkowski_problem wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Minkowski_problem wikiPageWikiLink Compact_space.
- Minkowski_problem wikiPageWikiLink Differential_geometry.
- Minkowski_problem wikiPageWikiLink Diffraction.
- Minkowski_problem wikiPageWikiLink Dirichlet_problem.
- Minkowski_problem wikiPageWikiLink Electromagnetic_radiation.
- Minkowski_problem wikiPageWikiLink Electromagnetic_wave.
- Minkowski_problem wikiPageWikiLink Elliptic_partial_differential_equation.
- Minkowski_problem wikiPageWikiLink Euclidean_space.
- Minkowski_problem wikiPageWikiLink Eugenio_Calabi.
- Minkowski_problem wikiPageWikiLink Fields_Medal.
- Minkowski_problem wikiPageWikiLink Gaussian_curvature.
- Minkowski_problem wikiPageWikiLink Global_differential_geometry.
- Minkowski_problem wikiPageWikiLink Hermann_Minkowski.
- Minkowski_problem wikiPageWikiLink International_Congress_of_Mathematicians.
- Minkowski_problem wikiPageWikiLink Mathematische_Annalen.
- Minkowski_problem wikiPageWikiLink Monge–Ampère_equation.
- Minkowski_problem wikiPageWikiLink Petr_Ufimtsev.
- Minkowski_problem wikiPageWikiLink Radiolocation.
- Minkowski_problem wikiPageWikiLink Riemannian_geometry.
- Minkowski_problem wikiPageWikiLink Riemannian_space.
- Minkowski_problem wikiPageWikiLink Rosetta_Stone.
- Minkowski_problem wikiPageWikiLink Shevchenko_National_Prize.
- Minkowski_problem wikiPageWikiLink Shing-Tung_Yau.
- Minkowski_problem wikiPageWikiLink Stealth-aircraft.
- Minkowski_problem wikiPageWikiLink Stealth_aircraft.
- Minkowski_problem wikiPageWikiLink Surface.
- Minkowski_problem wikiPageWikiLinkText "Minkowski problem".
- Minkowski_problem hasPhotoCollection Minkowski_problem.
- Minkowski_problem wikiPageUsesTemplate Template:Cite_book.
- Minkowski_problem wikiPageUsesTemplate Template:Cite_journal.
- Minkowski_problem wikiPageUsesTemplate Template:Reflist.
- Minkowski_problem subject Category:Differential_geometry.
- Minkowski_problem subject Category:Partial_differential_equations.
- Minkowski_problem subject Category:Theorems_in_geometry.
- Minkowski_problem type Article.
- Minkowski_problem type Article.
- Minkowski_problem type Physic.
- Minkowski_problem type Theorem.
- Minkowski_problem comment "In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface S whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly positive real function ƒ defined on a sphere, and the surface that is to be constructed should have Gaussian curvature ƒ(n(x)) at the point x, where n(x) denotes the normal to S at x.".
- Minkowski_problem label "Minkowski problem".
- Minkowski_problem sameAs m.0ch297g.
- Minkowski_problem sameAs Задача_Минковского.
- Minkowski_problem sameAs Задача_Мінковського.
- Minkowski_problem sameAs Q4183831.
- Minkowski_problem sameAs Q4183831.
- Minkowski_problem wasDerivedFrom Minkowski_problem?oldid=674550608.
- Minkowski_problem isPrimaryTopicOf Minkowski_problem.