The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets.
It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces.
It is related to, although different from, the Hausdorff measure.
The Minkowskicontent (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure...
Hermann Minkowski (/mɪŋˈkɔːfski, -ˈkɒf-/ ming-KAWF-skee, -KOF-; German: [mɪŋˈkɔfski]; 22 June 1864 – 12 January 1909) was a German mathematician and...
for irregular objects of any dimension. An important example is the Minkowskicontent of a surface. While the areas of many simple surfaces have been known...
where M ∗ n − 1 {\displaystyle M_{*}^{n-1}} is the (n-1)-dimensional Minkowskicontent, Ln is the n-dimensional Lebesgue measure, and ωn is the volume of...
and infinity. In geometric measure theory and related fields, the Minkowskicontent is often used to measure the size of a subset of a metric measure...
is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension. The intuitive concept of dimension of a geometric...
indicator function of a set is Gaussian surface area, which is the Minkowskicontent of the boundary of the set. The counterpart of the noise operator...
binds to the elastic tissue of the skin and sclera, where high albumin content can be found. This explains the yellow discolouration observed in these...
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...
Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused...
spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe can be modeled as a pseudo-Riemannian manifold...
proposed by Albert Einstein and subsequent work of Max Planck, Hermann Minkowski and others. Although Isaac Newton based his physics on absolute time and...
mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational)...
isotropy, and memorylessness. Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed...
not a Minkowski space, but rather a de Sitter space with a positive cosmological constant.: 30 In a de Sitter vacuum (but not in a Minkowski vacuum)...
of things named after John Milnor List of things named after Hermann Minkowski List of things named after John von Neumann List of things named after...
intervened for this theory". In addition, the spacetime formulation by Hermann Minkowski in 1907 was influential in gaining widespread acceptance. Also, and most...
theory of relativity. The local reduction of the metric tensor to the Minkowski metric tensor corresponds to free-falling (geodesic) motion, in this theory...
Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov...
left with the Minkowski distance formula, which can be used in a wide variety of applications. Euclidean distance Manhattan distance Minkowski distance Chebyshev...
the geometry of numbers. He used the results of Evgraf Fedorov, Hermann Minkowski, Georgy Voronoy, and others in his development of modern mathematical...
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