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- Minkowski_problem abstract "In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks, for a given strictly positive real function ƒ defined on sphere, for a strictly convex compact surface S whose Gaussian curvature at the point x equals ƒ(n(x)), where n(x) denotes the normal to S at x. Eugenio Calabi stated: "From the geometric view point the Minkowski problem is the Rosetta Stone, from which several related problems can be solved."[citation needed]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 wikiPageRevisionID "603815712".
- Minkowski_problem hasPhotoCollection Minkowski_problem.
- Minkowski_problem subject Category:Differential_geometry.
- Minkowski_problem subject Category:Partial_differential_equations.
- Minkowski_problem subject Category:Theorems_in_geometry.
- Minkowski_problem type Abstraction100002137.
- Minkowski_problem type Communication100033020.
- Minkowski_problem type DifferentialEquation106670521.
- Minkowski_problem type Equation106669864.
- Minkowski_problem type MathematicalStatement106732169.
- Minkowski_problem type Message106598915.
- Minkowski_problem type PartialDifferentialEquation106670866.
- Minkowski_problem type PartialDifferentialEquations.
- Minkowski_problem type Proposition106750804.
- Minkowski_problem type Statement106722453.
- Minkowski_problem type Theorem106752293.
- Minkowski_problem type TheoremsInGeometry.
- Minkowski_problem comment "In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks, for a given strictly positive real function ƒ defined on sphere, for a strictly convex compact surface S whose Gaussian curvature at the point x equals ƒ(n(x)), where n(x) denotes the normal to S at x.".
- Minkowski_problem label "Minkowski problem".
- Minkowski_problem label "Задача Минковского".
- Minkowski_problem sameAs m.0ch297g.
- Minkowski_problem sameAs Q4183831.
- Minkowski_problem sameAs Q4183831.
- Minkowski_problem sameAs Minkowski_problem.
- Minkowski_problem wasDerivedFrom Minkowski_problem?oldid=603815712.
- Minkowski_problem isPrimaryTopicOf Minkowski_problem.