Minkowski problem, the Glossary

Table of Contents

1. 33 relations: Aleksandr Aleksandrov (mathematician), Aleksei Pogorelov, Børge Jessen, Bulletin of the American Mathematical Society, Calabi conjecture, Communications on Pure and Applied Mathematics, Compact space, Convex body, Differential geometry, Diffraction, Dirichlet problem, Elliptic partial differential equation, Euclidean space, Eugenio Calabi, Fields Medal, Gauss map, Gaussian curvature, Herbert Busemann, Hermann Minkowski, International Congress of Mathematicians, Louis Nirenberg, Mathematische Annalen, Michigan Mathematical Journal, Monge–Ampère equation, Project Euclid, Radiolocation, Riemannian geometry, Rosetta Stone, Shevchenko National Prize, Shing-Tung Yau, Shiu-Yuen Cheng, Surface (topology), Werner Fenchel.

2. Hermann Minkowski
3. Theorems in geometry

Aleksandr Aleksandrov (mathematician)

Aleksandr Danilovich Aleksandrov (Алекса́ндр Дани́лович Алекса́ндров, alternative transliterations: Alexandr or Alexander (first name), and Alexandrov (last name)) (4 August 1912 – 27 July 1999) was a Soviet/Russian mathematician, physicist, philosopher and mountaineer.

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Aleksei Pogorelov

Aleksei Vasilyevich Pogorelov (Алексе́й Васи́льевич Погоре́лов, Олексі́й Васи́льович Погорє́лов; 3 March 1919 – 17 December 2002), was a Soviet mathematician.

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Børge Jessen

Børge Christian Jessen (19 June 1907 – 20 March 1993) was a Danish mathematician best known for his work in analysis, specifically on the Riemann zeta function, and in geometry, specifically on Hilbert's third problem.

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Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

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Calabi conjecture

In the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on certain complex manifolds, made by.

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Communications on Pure and Applied Mathematics

Communications on Pure and Applied Mathematics is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences.

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Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

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Convex body

In mathematics, a convex body in n-dimensional Euclidean space \R^n is a compact convex set with non-empty interior.

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Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.

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Diffraction

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture.

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Dirichlet problem

In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. Minkowski problem and Dirichlet problem are partial differential equations.

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Elliptic partial differential equation

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Minkowski problem and elliptic partial differential equation are partial differential equations.

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Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

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Eugenio Calabi

Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications.

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Fields Medal

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

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Gauss map

In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface at that point. Minkowski problem and Gauss map are differential geometry.

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and, at the given point: K. Minkowski problem and Gaussian curvature are differential geometry.

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Herbert Busemann

Herbert Busemann (12 May 1905 – 3 February 1994) was a German-American mathematician specializing in convex and differential geometry.

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Hermann Minkowski

Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, or Lithuanian-German, or Russian.

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International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics.

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Louis Nirenberg

Louis Nirenberg (February 28, 1925 – January 26, 2020) was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.

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Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

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Michigan Mathematical Journal

The Michigan Mathematical Journal (established 1952) is published by the mathematics department at the University of Michigan.

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Monge–Ampère equation

In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. Minkowski problem and Monge–Ampère equation are partial differential equations.

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Project Euclid

Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent and society publishers.

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Radiolocation

Radiolocation, also known as radiolocating or radiopositioning, is the process of finding the location of something through the use of radio waves.

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Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). Minkowski problem and Riemannian geometry are differential geometry.

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Rosetta Stone

The Rosetta Stone is a stele of granodiorite inscribed with three versions of a decree issued in 196 BC during the Ptolemaic dynasty of Egypt, on behalf of King Ptolemy V Epiphanes.

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Shevchenko National Prize

Shevchenko National Prize (Націона́льна пре́мія Украї́ни і́мені Тараса́ Шевче́нка; also Shevchenko Award) is the highest state prize of Ukraine for works of culture and arts awarded since 1961.

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Shing-Tung Yau

Shing-Tung Yau (born April 4, 1949) is a Chinese-American mathematician.

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Shiu-Yuen Cheng

Shiu-Yuen Cheng (鄭紹遠) is a Hong Kong mathematician.

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Surface (topology)

In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.

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Werner Fenchel

Moritz Werner Fenchel (3 May 1905 – 24 January 1988) was a German-born Danish mathematician known for his contributions to geometry and to optimization theory.

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See also

Hermann Minkowski

• Abraham–Minkowski controversy
• Brunn–Minkowski theorem
• Hasse–Minkowski theorem
• Hermann Minkowski
• Hyperplane separation theorem
• Minkowski (crater)
• Minkowski addition
• Minkowski content
• Minkowski distance
• Minkowski functional
• Minkowski problem
• Minkowski problem for polytopes
• Minkowski sausage
• Minkowski space
• Minkowski's bound
• Minkowski's question-mark function
• Minkowski's second theorem
• Minkowski's theorem
• Minkowski–Bouligand dimension
• Minkowski–Hlawka theorem
• Minkowski–Steiner formula
• Smith–Minkowski–Siegel mass formula

Theorems in geometry

• 2π theorem
• Almgren regularity theorem
• Anderson's theorem
• Bang's theorem on tetrahedra
• Beckman–Quarles theorem
• Bernstein–Kushnirenko theorem
• Blichfeldt's theorem
• Campbell's theorem (geometry)
• Castelnuovo's contraction theorem
• Castelnuovo–de Franchis theorem
• Chow–Rashevskii theorem
• Collage theorem
• Commandino's theorem
• Dévissage
• De Gua's theorem
• Dodecahedral conjecture
• Double limit theorem
• Euler's rotation theorem
• Fold-and-cut theorem
• Hyperbolization theorem
• Jørgensen's inequality
• Jung's theorem
• Lickorish–Wallace theorem
• Liouville's theorem (conformal mappings)
• Minkowski problem
• Minkowski–Hlawka theorem
• Mostow rigidity theorem
• Murakami–Yano formula
• Niven's theorem
• Non-squeezing theorem
• Pappus's centroid theorem
• Petersen–Morley theorem
• Principal axis theorem
• Reshetnyak gluing theorem
• Riemannian Penrose inequality
• Shapley–Folkman lemma
• Skoda–El Mir theorem
• Soddy's hexlet
• Spherical law of cosines
• Tameness theorem
• Theorem of the cube
• Theorema Egregium
• Thom conjecture
• Triangle inequality
• Ultraparallel theorem
• Wendel's theorem

References

[1] https://en.wikipedia.org/wiki/Minkowski_problem