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Constructing a strictly convex compact surface with specified Gaussian curvature
In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface S whose
Minkowski_problem
In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures
Minkowski problem for polytopes
Minkowski_problem_for_polytopes
German mathematician and physicist (1864–1909)
Minkowski (crater) Minkowski distance Minkowski functional Minkowski inequality Minkowski model Minkowski plane Minkowski problem Minkowski problem for polytopes
Hermann_Minkowski
Chinese-American mathematician (born 1949)
integrable unless it is constant.[Y76] The Minkowski problem of classical differential geometry can be viewed as the problem of prescribing Gaussian curvature
Shing-Tung_Yau
Hong Kong mathematician
an embedding of the n-dimensional sphere, via the Gauss map. The Minkowski problem asks whether an arbitrary smooth and positive function on the n-dimensional
Shiu-Yuen_Cheng
Mathematical description of spacetime used in relativity
In physics, Minkowski spacetime (or Minkowski space; /mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation
Minkowski_spacetime
Canadian-American mathematician (1925–2020)
fluid mechanics. Other achievements include the resolution of the Minkowski problem in two-dimensions, the Gagliardo–Nirenberg interpolation inequality
Louis_Nirenberg
Minkowski content Minkowski distance Minkowski functional Minkowski inequality Minkowski model Minkowski plane Minkowski problem Minkowski problem for polytopes
List of things named after Hermann Minkowski
List_of_things_named_after_Hermann_Minkowski
Field of higher mathematics
manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei
Geometric_analysis
Sums vector sets A and B by adding each vector in A to each vector in B
Minkowski sum depends on the choice of an origin in the Euclidean space. As a change of origin amounts to translate the Minkowski sum, the Minkowski sum
Minkowski_addition
necessarily have Hausdorff dimension and Minkowski dimension equal to n {\displaystyle n} ? The Kelvin problem on minimum-surface-area partitions of space
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
American mathematician
and Deane Yang) to the Lp Brunn Minkowski Theory and, in particular, his solution to the logarithmic Minkowski problem. Zhang, Gaoyong (1991), "Restricted
Gaoyong_Zhang
American mathematician
surface area, his contributions to the Lp Brunn Minkowski Theory and, in particular, his Lp Minkowski problem and its solution in important cases. Lutwak
Erwin_Lutwak
Polytope combining two smaller polytopes
unique up to translation, as can be proven using the theory of the Minkowski problem for polytopes. They can be used to decompose arbitrary polytopes into
Blaschke_sum
Graph of space and time in special relativity
class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that
Spacetime_diagram
Mathematical model combining space and time
Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused
Spacetime
Philosophical thought experiment
is not a Minkowski space, but rather a de Sitter space with a positive cosmological constant. In a de Sitter vacuum (but not in a Minkowski vacuum), a
Boltzmann_brain
German mathematician (1862–1943)
the University of Königsberg, the "Albertina". In early 1882, Hermann Minkowski (two years younger than Hilbert and also a native of Königsberg but had
David_Hilbert
In mathematics, the Minkowski–Steiner formula is a formula relating the surface area and volume of compact subsets of Euclidean space. More precisely
Minkowski–Steiner_formula
Every symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to
Minkowski's_theorem
Geometric inequality applicable to any closed curve
manifolds. However, the isoperimetric problem can be formulated in much greater generality, using the notion of Minkowski content. Let ( X , μ , d ) {\displaystyle
Isoperimetric_inequality
Nonlinear second-order partial differential equation of special kind
a solution, if any. The problem of finding a solution is the Minkowski problem, or the prescribed Gaussian curvature problem. For example, the rigidity
Monge–Ampère_equation
Application of geometry in number theory
unsolved problem prior to Minkowski's work. Related geometric arguments supply an alternative proof of the Dirichlet unit theorem. Minkowski's construction
Geometry_of_numbers
Shape containing unit line segments in all directions
that the Minkowski dimension of Kakeya sets in 3 dimensions is strictly greater than 5/2. In 2000, Jean Bourgain connected the Kakeya problem to arithmetic
Kakeya_set
Field-equations in general relativity
and the spacetime approximates that of Minkowski space. The metric is then written as the sum of the Minkowski metric and a term representing the deviation
Einstein_field_equations
methods of Shiu-Yuen Cheng and Shing-Tung Yau's resolution of the Minkowski problem to study the higher-dimensional version of Gage and Hamilton's result
Gauss_curvature_flow
General-relativistic effect
effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity
Gravitational_time_dilation
Criteria of simplicity for mathematical proofs
presenting Hilbert's problems or any published texts. Hilbert's friends and fellow mathematicians Adolf Hurwitz and Hermann Minkowski were closely involved
Hilbert's twenty-fourth problem
Hilbert's_twenty-fourth_problem
Compact astronomical body
Hubble Space Telescope. Unsolved problem in physics Is physical information lost in black holes? More unsolved problems in physics According to the no-hair
Black_hole
Path of an object through spacetime
world lines was originated by physicists and was pioneered by Hermann Minkowski. The term is now used most often in the context of relativity theories
World_line
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Thought experiment in special relativity
constant velocity motion, all of which was visualized by Thirring using Minkowski diagrams. The same result was already before obtained by Einstein (1918)
Twin_paradox
In geometry, set whose intersection with every line is a single line segment
hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski theory. Encyclopedia
Convex_set
Chinese-Australian mathematician
Kai-Seng Chou) Chou, Kai-Seng; Wang, Xu-Jia (2006). "The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry". Advances in Mathematics. 205
Xu-Jia_Wang
Measured time difference as explained by relativity theory
first to point out its reciprocity or symmetry. Subsequently, Hermann Minkowski (1907) introduced the concept of proper time which further clarified the
Time_dilation
Function with unusual fractal properties
mathematics, Minkowski's question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. It
Minkowski's question-mark function
Minkowski's_question-mark_function
Two quadratic forms over a number field are equivalent iff they are equivalent locally
The Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only
Hasse–Minkowski_theorem
Construct all metric spaces where lines resemble those on a sphere
proved by E. Cartan in 1930. In 1890, for solving problems on the theory of numbers, Hermann Minkowski introduced a notion of the space that nowadays is
Hilbert's_fourth_problem
Two interrelated physics theories by Albert Einstein
Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work. Einstein developed general relativity
Theory_of_relativity
German-American astronomer
Rudolph Minkowski (born Rudolf Leo Bernhard Minkowski /mɪŋˈkɔːfski, -ˈkɒf-/; German: [mɪŋˈkɔfski]; May 28, 1895 – January 4, 1976) was a German-American
Rudolph_Minkowski
Hamiltonian formulation of general relativity
at infinity – for example a spacetime that asymptotically approaches Minkowski space. The ADM energy in these cases is defined as a function of the deviation
ADM_formalism
Measure of relativistic velocity
that is, the interval −c < v < c maps onto −∞ < w < ∞. In 1908 Hermann Minkowski explained how the Lorentz transformation could be seen as simply a hyperbolic
Rapidity
French psychiatrist (1885–1972)
Eugène Minkowski (French: [øʒɛn mɛ̃kɔfski]; born Eugeniusz Minkowski; 17 April 1885 – 17 November 1972) was a French psychiatrist of Jewish Polish origin
Eugène_Minkowski
Hypothetical topological feature of spacetime
taken from Matt Visser's Lorentzian Wormholes (1996).[page needed] If a Minkowski spacetime contains a compact region Ω {\displaystyle \Omega } , and if
Wormhole
Method of determining fractal dimension
In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal
Minkowski–Bouligand_dimension
Set of spacetime events, light-connected to a given event
Hermann Minkowski and is known as Minkowski space. The purpose was to create an invariant spacetime for all observers. To uphold causality, Minkowski restricted
Light_cone
Theorem in geometric number theory
In mathematics, Minkowski's second theorem is a result in the geometry of numbers about the values taken by a norm on a lattice and the volume of its
Minkowski's_second_theorem
Problems which attempt to find the most efficient way to pack objects into containers
arXiv:math/9909172. doi:10.1016/S0925-7721(00)00007-9. MR 1765181. S2CID 12118403. Minkowski, H. Dichteste gitterförmige Lagerung kongruenter Körper. Nachr. Akad.
Packing_problems
Family of linear transformations
a rotation-free Lorentz transformation is called a Lorentz boost. In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz
Lorentz_transformation
Condition in which spacetime itself breaks down
(returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox. However, processes inside
Gravitational_singularity
Existence theorem on the lattice packing of hyperspheres
In mathematics, the Minkowski–Hlawka theorem is a result on the lattice packing of hyperspheres in dimension n > 1. It states that there is a lattice
Minkowski–Hlawka_theorem
Hypothetical quantum cosmological effect
can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must
Hawking_radiation
Solution of Einstein field equations
special directions were not geodesics of the underlying Minkowski space proved very difficult. The problem was given to George Debney to try to solve but was
Kerr–Newman_metric
German mathematician (1885–1955)
mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well
Hermann_Weyl
Problematic appearance of quantities beyond the Planck scale
effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial. Brandenberger, Robert (2011).
Trans-Planckian_problem
Shiu-Yuen Cheng and Shing-Tung Yau resolved the Bernstein problem for maximal surfaces of Minkowski space which are properly embedded, showing that any such
Maximal_surface
Diagram of different points in spacetime
(suitable for the curved spacetimes of e.g. general relativity) of the Minkowski diagram of special relativity where the vertical dimension represents
Penrose_diagram
Concept that simultaneity depends on choice of reference frame
1908, Hermann Minkowski introduced the concept of a world line of a particle in his model of the cosmos called Minkowski space. In Minkowski's view, the naïve
Relativity_of_simultaneity
Finnish mathematician (1965–2020)
Inverse problems of generalized projection operators. Inverse Problems 22, 749. L. Lamberg and M. Kaasalainen (2001): Numerical solution of the Minkowski problem
Mikko_Kaasalainen
German–British physicist (1882–1970)
three renowned mathematicians Felix Klein, David Hilbert, and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of the stability of elastic
Max_Born
Region in spacetime from which nothing can escape
paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space General relativity Background Introduction Mathematical
Event_horizon
Key result in general relativity
can define the energy-momentum of each infinite region as an element of Minkowski space. Provided that the initial data set is geodesically complete and
Positive_energy_theorem
Physics concept expressed as E = mc²
was no need for fictitious masses. He could avoid the perpetual motion problem because, on the basis of the mass–energy equivalence, he could show that
Mass–energy_equivalence
Light bending by mass between source and observer
paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space General relativity Background Introduction Mathematical
Gravitational_lens
Classify quadratic forms over algebraic number fields
Kaplansky, "The 11th Problem is simply this: classify quadratic forms over algebraic number fields." This is exactly what Minkowski did for quadratic form
Hilbert's_eleventh_problem
Generalization of straight line to a curved space time
longer or a shorter proper length than the geodesic, even in Minkowski space. In Minkowski space, the geodesic will be a straight line. Any curve that
Geodesics in general relativity
Geodesics_in_general_relativity
Contraction of length in the direction of propagation in Minkowski space
transformation apply to both electromagnetism and mechanics. Hermann Minkowski gave the geometrical interpretation of all relativistic effects by introducing
Length_contraction
Natural number
(2019). "Cracking the problem with 33". arXiv:1903.04284 [math.NT]. Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory
33_(number)
Hypothetical object of spacetime
effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity
White_hole
Differentiable manifold with nondegenerate metric tensor
model of a Riemannian manifold, Minkowski space R n − 1 , 1 {\displaystyle \mathbb {R} ^{n-1,1}} with the flat Minkowski metric is the local model of a
Pseudo-Riemannian_manifold
Tensor describing energy momentum density in spacetime
gravity. The electromagnetic stress–energy tensor was introduced by Hermann Minkowski in 1907, and later generalized by Max von Laue in 1911. The stress–energy
Stress–energy_tensor
Trace radiation from the early universe
in the data. Ultimately, due to the foregrounds and the cosmic variance problem, the greatest modes will never be as well measured as the small angular
Cosmic_microwave_background
Reinhard Meinel (Neugebauer–Meinel dust disk solution), Hermann Minkowski (Minkowski spacetime), Charles W. Misner (mixmaster model, ADM initial value
List of contributors to general relativity
List_of_contributors_to_general_relativity
French mathematician, physicist and engineer (1854–1912)
geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907. Like others before
Henri_Poincaré
Solution to the Einstein field equations
Schwarzschild metric is asymptotic to the standard Lorentz metric on Minkowski space. For almost all astrophysical objects, the ratio r s R {\displaystyle
Schwarzschild_metric
Theory of interwoven space and time by Albert Einstein
special relativity was recast by Hermann Minkowski in a 4-dimensional geometry now called Minkowski space. Minkowski spacetime appears to be very similar
Special_relativity
Exact solution for the Einstein field equations
g and η. Here M is the constant mass of the spinning object, η is the Minkowski tensor, and a is a constant rotational parameter of the spinning object
Kerr_metric
Geometric space with four dimensions
appropriate to electromagnetic relations in his cosmos. Minkowski's world overcame problems associated with the traditional absolute space and time cosmology
Four-dimensional_space
nonlinear Schrödinger equation (NLS). But recall that the conformal group on Minkowski spacetime is the symmetry group of the Maxwell equations. Recall too that
Exact solutions in general relativity
Exact_solutions_in_general_relativity
Mathematical problem
additional restrictions on the attainability of the bound using the Hasse–Minkowski theorem on the rational equivalence of quadratic forms, and showed that
Hadamard's maximal determinant problem
Hadamard's_maximal_determinant_problem
Hypothetical FTL transportation by warping space
Alcubierre drive remains a hypothetical concept with seemingly difficult problems, although the amount of energy required is no longer thought to be unobtainably
Alcubierre_drive
Soviet and Russian mathematician
of convex surfaces. AMS. 1973. The Minkowski multidimensional problem. V. H. Winston. 1978. Hilbert's fourth problem. V. H. Winston. 1979. Bending of surfaces
Aleksei_Pogorelov
Equations in physical cosmology
paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space General relativity Background Introduction Mathematical
Friedmann_equations
English mathematician, mathematical physicist (born 1931)
Penrose invented the twistor theory, which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2
Roger_Penrose
Mathematical trick using imaginary numbers to simplify certain formulas in physics
method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation
Wick_rotation
Effect of general relativity
paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space General relativity Background Introduction Mathematical
Frame-dragging
Solution of Einstein field equations
effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity
Gödel_metric
Abstract coordinate system
coefficients in a functional expansion like a Fourier series. In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot
Frame_of_reference
Mathematical object that describes the electromagnetic field in spacetime
four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The EM tensor allows related physical laws to be written concisely, and
Electromagnetic_tensor
Equation explaining structure of a spherical body of isotropic material
effect Event horizon Singularity Black hole Spacetime Spacetime diagrams Minkowski spacetime Metric tensor Equations Formalisms Equations Linearized gravity
Tolman–Oppenheimer–Volkoff equation
Tolman–Oppenheimer–Volkoff_equation
Method of drawing geometric objects
constructions appear to be a parlour game, rather than a serious practical problem. However, the restrictions' purpose is to ensure that constructions can
Straightedge and compass construction
Straightedge_and_compass_construction
Aspect of relativity in physics
Lightman, A.P.; Press, W.H.; Price, R.H.; Teukolsky, S.A. (1975). "Problem 12.16". Problem book in Relativity and Gravitation. Princeton University Press
Gravitational_wave
Exact solution to the Einstein field equations
accepted as correct. This led Oppenheimer to consider the natural next problem of determining what would happen if a neutron star were so heavy it would
Oppenheimer–Snyder_model
Exact solution in general relativity
/ r {\displaystyle r_{\text{s}}/r} go to zero, the metric becomes the Minkowski metric for special relativity. In practice, the ratio r s / r {\displaystyle
Reissner–Nordström_metric
Convex polyhedron projected from hypercube
symmetric (a zonogon). Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as a three-dimensional
Zonohedron
Computational problem
path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations
Motion_planning
Perimeter of a circle or ellipse
Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi
Circumference
Physics principle
will call the principle of relativity." Einstein, A.; Lorentz, H. A.; Minkowski, H.; Weyl, H. (1952) [1923]. Arnold Sommerfeld (ed.). The Principle of
Principle_of_relativity
German-born theoretical physicist (1879–1955)
In 1908, Hermann Minkowski reinterpreted special relativity in geometric terms as a theory of spacetime. Einstein adopted Minkowski's formalism in his
Albert_Einstein
Theory of rapid universe expansion
Gunzig suggested that the universe could originate from a fluctuation of Minkowski space which would be followed by a period in which the geometry would
Cosmic_inflation
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Girl/Female
Indian, Telugu
Destroyer of Problems
Boy/Male
Muslim
Problem solver
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Hindu, Indian
Problem
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
Girl/Female
Gaelic
Ewe.
Girl/Female
Hindu, Indian
Daisy in a Field of Roses
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Goddess Lakshmi; One who Got Blessings
Boy/Male
British, English
Stag Meadow
Boy/Male
Tamil
Leelakar | லீலாகரÂ
Lord Krishna
Female
English
Variant spelling of English Izzy, IZZIE means "God is my oath."
Boy/Male
Hindu
Deep water
Surname or Lastname
English
English : unexplained.
Boy/Male
Hawaiian
Protector.
Female
English
Feminine form of English Adrian, ADRIANNAH means "from Hadria."
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
MINKOWSKI PROBLEM
n.
A problem of more than usual difficulty added to another on an examination paper.
a.
Single; not complex; not infolded or entangled; uncombined; not compounded; not blended with something else; not complicated; as, a simple substance; a simple idea; a simple sound; a simple machine; a simple problem; simple tasks.
n.
To cause to stick; to bring to a stand; to pose; to puzzle; as, to stick one with a hard problem.
n.
An instrument of the ancients for finding two mean proportionals between two given lines, required in solving the problem of the duplication of the cube.
n.
A problem to be solved, or an example to be wrought out.
v. t.
To propose problems.
a.
Questionable; equivocal; indefinite; problematical.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
v. t.
To explain; to resolve; to unfold; to clear up (what is obscure or difficult to be understood); to work out to a result or conclusion; as, to solve a doubt; to solve difficulties; to solve a problem.
a.
Alt. of Problematical
a.
Liable to question; subject to be doubted or called in question; problematical; doubtful; suspicious.
a.
Susceptible of being solved; as, a soluble algebraic problem; susceptible of being disentangled, unraveled, or explained; as, the mystery is perhaps soluble.
n.
The quality, condition, or degree of being soluble or solvable; as, the solubility of a salt; the solubility of a problem or intricate difficulty.
n.
To begin to deal with; as, to tackle the problem.
v. i.
To work, as at a puzzle; as, to puzzle over a problem.
n.
One who proposes problems.
a.
Having the nature of a problem; not shown in fact; questionable; uncertain; unsettled; doubtful.
v. t.
To have just and adequate ideas of; to apprehended the meaning or intention of; to have knowledge of; to comprehend; to know; as, to understand a problem in Euclid; to understand a proposition or a declaration; the court understands the advocate or his argument; to understand the sacred oracles; to understand a nod or a wink.
n.
The quality or state of being solvable; as, the solvability of a difficulty; the solvability of a problem.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.