In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures)...
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fundamental in the Lp Brunn-Minkowski theory. Blaschke sum – Polytope combining two smaller polytopes Brunn–Minkowski theorem – theorem in geometryPages displaying...
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Hermann Minkowski Abraham–Minkowski controversy Brunn–Minkowski theorem Hasse–Minkowski theorem Hermite–Minkowski theorem Minkowski addition Minkowski (crater)...
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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...
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mathematics, Vitale's random Brunn–Minkowski inequality is a theorem due to Richard Vitale that generalizes the classical Brunn–Minkowski inequality for compact...
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Milman's reverse Brunn–Minkowski inequality is a result due to Vitali Milman that provides a reverse inequality to the famous Brunn–Minkowski inequality for...
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Minkowski (1864 - 1909), German mathematician: Brunn–Minkowski theorem Hasse–Minkowski theorem Hermite–Minkowski theorem Minkowski addition Minkowski...
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volume in an appropriate sense. The Minkowski–Steiner formula is used, together with the Brunn–Minkowski theorem, to prove the isoperimetric inequality...
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Determinant (redirect from Determinant theorem)
B ) . {\displaystyle \det(A+B)\geq \det(A)+\det(B){\text{.}}} Brunn–Minkowski theorem implies that the nth root of determinant is a concave function...
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Brun–Titchmarsh theorem (number theory) Brunn–Minkowski theorem (Riemannian geometry) Büchi-Elgot-Trakhtenbrot theorem (mathematical logic) Buckingham π theorem (dimensional...
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body in S⊥. Brunn–Minkowski inequality Prékopa–Leindler inequality Busemann, Herbert (1949). "A theorem on convex bodies of the Brunn-Minkowski type". Proc...
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type of duality relation. List of convexity topics John ellipsoid Brunn–Minkowski theorem, which has many implications relevant to the geometry of convex...
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origin-symmetric convex body K ⊆ Rn. Gardner, Richard J. (2002). "The Brunn-Minkowski inequality". Bull. Amer. Math. Soc. (N.S.). 39 (3): 355–405 (electronic)...
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inequality Milman's reverse Brunn–Minkowski inequality Milnor–Wood inequality Minkowski's first inequality for convex bodies Myers's theorem Noether inequality...
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Geometry of numbers (section Minkowski's results)
{\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 ( R...
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Convex set (section Convex hulls and Minkowski sums)
hulls of Minkowski sumsets in its "Chapter 3 Minkowski addition" (pages 126–196): Schneider, Rolf (1993). Convex bodies: The Brunn–Minkowski theory. Encyclopedia...
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as the Kneser–Süss inequality, an analogue of the Brunn–Minkowski theorem on volumes of Minkowski sums of convex bodies: V ( X # Y ) ( d − 1 ) / d ≥...
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isoperimetric inequality. The Brunn–Minkowski inequality also leads to Anderson's theorem in statistics. The proof of the Brunn–Minkowski inequality predates modern...
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minimization Fenchel's duality theorem Geometry Convex geometry Brunn–Minkowski theorem Differential geometry Fenchel's theorem Hyperbolic geometry Jakob Nielsen...
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Isoperimetric inequality (redirect from Isoperimetric theorem)
may be a curve. The proof of the inequality follows directly from Brunn–Minkowski inequality between a set S {\displaystyle S} and a ball with radius...
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Prékopa–Leindler inequality (category Theorems in analysis)
inequality closely related to the reverse Young's inequality, the Brunn–Minkowski inequality and a number of other important and classical inequalities...
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Shapley–Folkman lemma (redirect from Shapley-Folkman theorem)
For example, the Shapley–Folkman theorem provides an upper bound on the distance between any point in the Minkowski sum and its convex hull. This upper...
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Convex hull (section Minkowski sum)
1016/0022-0531(77)90095-3 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44,...
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Numerous geometric inequalities, such as the Brunn–Minkowski inequality for convex bodies and Minkowski's first inequality, are special cases of the Alexandrov–Fenchel...
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Zonohedron (section Zonohedra from Minkowski sums)
"Zonoids and other classes of convex bodies" in Convex bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993. Shephard, G. C...
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William J. (1961). "Polar Means of Convex Bodies and a Dual to the Brunn-Minkowski Theorem". Canadian Journal of Mathematics. 13: 444–453. doi:10.4153/CJM-1961-037-0...
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Convex Bodies: the Brunn-Minkowski Theory, Cambridge: Cambridge University Press Nirenberg, L. (1953). "The Weyl and Minkowski problems in differential...
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Lusternik–Schnirelmann category Lyusternik's generalization of the Brunn–Minkowski theorem Pavel Alexandrov et al., LAZAR' ARONOVICH LYUSTERNIK (on the occasion...
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(B)^{1-\lambda },} where λ A + (1 − λ) B denotes the Minkowski sum of λ A and (1 − λ) B. The Brunn–Minkowski inequality asserts that the Lebesgue measure is...
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location missing publisher (link) Gardner, Richard J. (2002). "The Brunn–Minkowski inequality". Bull. Amer. Math. Soc. (N.S.). 39 (3): 355–405 (electronic)...
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