In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number...

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...

polytopes Minkowski's second theorem Minkowski space Minkowski's bound Minkowski's theorem in geometry of numbers Minkowski–Hlawka theorem Minkowski–Steiner...

class group of a quadratic field extension can be accomplished using Minkowski's bound and the Kronecker symbol because of the finiteness of the class group...

Demonstrations Project. Minkowski's addition of convex shapes by Alexander Bogomolny: an applet Wikibooks:OpenSCAD User Manual/Transformations#minkowski by Marius Kintel:...

bodies Minkowski's question mark function Minkowski's second theorem Minkowski's theorem in geometry of numbers Minkowski–Bouligand dimension Minkowski cover...

}{4}}\right)^{n/2}.} Minkowski's theorem: If K is not Q, then |ΔK| > 1 (this follows directly from the Minkowski bound). Hermite–Minkowski theorem: Let N be...

lower bound of S {\displaystyle S} , then b is less than or equal to the infimum of S {\displaystyle S} . Consequently, the term greatest lower bound (abbreviated...

using Minkowski's bound. This result gives a bound, depending on the ring, such that every ideal class contains an ideal norm less than the bound. In general...

Hermann Minkowski; it has been called "Minkowski's theorem", although the same name has also been given to several unrelated results of Minkowski. The Minkowski...

In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures)...

{\textstyle \lambda _{1}(L)\lambda _{1}(L^{*})\leq n} follows from Minkowski's bound on the shortest vector; that is, λ 1 ( L ) ≤ n ( det ( L ) 1 / n )...

inequality Melchior's inequality Milman's reverse Brunn–Minkowski inequality Milnor–Wood inequality Minkowski's first inequality for convex bodies Myers's theorem...

set in Rn, given as the image of a bounded set from Rm under a Lipschitz function, then the m-dimensional Minkowski content of A exists, and is equal to...

defined in terms of microscopic bound charges and bound currents respectively. The macroscopic bound charge density ρb and bound current density Jb in terms...

hull of a totally bounded subset of a topological vector space is again totally bounded. The Minkowski sum of two compact (totally bounded) sets is compact...

everywhere unramified extension of K, and it is abelian. Using the Minkowski bound, one can show that K has class number 2. Hence, its Hilbert class field...

proof by Hermann Minkowski (1911, pages 265–276) and proved by Edmund Hlawka (1943). The result is related to a linear lower bound for the Hermite constant...

{\displaystyle K} is a convex centrally symmetric body. Minkowski's theorem, sometimes called Minkowski's first theorem, states that if vol ⁡ ( K ) > 2 n vol...

Lebesgue measure and the + on the left-hand side denotes Minkowski addition. In general, no reverse bound is possible, since one can find convex bodies K and...

triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite...

called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called...

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...

In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base...

forgotten for many years. It was rediscovered by H. Minkowski (1885), and an error in Minkowski's paper was found and corrected by C. L. Siegel (1935)...

with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection...

with convex sets: every seminorm is the Minkowski functional of some absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm...

hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski theory. Encyclopedia...

Hermann Minkowski's Space–Time Formalism of Special Relativity". arXiv:1210.6929 [physics.hist-ph]. Galison, Peter Louis (1979). "Minkowski's space–time:...

theorem provides an upper bound on the distance between any point in the Minkowski sum and its convex hull. This upper bound is sharpened by the Shapley–Folkman–Starr...