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

fundamental in the Lp Brunn-Minkowski theory. Blaschke sum – Polytope combining two smaller polytopes Brunn–Minkowski theorem – theorem in geometryPages displaying...

Hermann Minkowski Abraham–Minkowski controversy Brunn–Minkowski theorem Hasse–Minkowski theorem Hermite–Minkowski theorem Minkowski addition Minkowski (crater)...

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...

mathematics, Vitale's random Brunn–Minkowski inequality is a theorem due to Richard Vitale that generalizes the classical Brunn–Minkowski inequality for compact...

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...

Minkowski (1864 - 1909), German mathematician: Brunn–Minkowski theorem Hasse–Minkowski theorem Hermite–Minkowski theorem Minkowski addition Minkowski...

volume in an appropriate sense. The Minkowski–Steiner formula is used, together with the Brunn–Minkowski theorem, to prove the isoperimetric inequality...

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...

Brun–Titchmarsh theorem (number theory) Brunn–Minkowski theorem (Riemannian geometry) Büchi-Elgot-Trakhtenbrot theorem (mathematical logic) Buckingham π theorem (dimensional...

body in S⊥. Brunn–Minkowski inequality Prékopa–Leindler inequality Busemann, Herbert (1949). "A theorem on convex bodies of the Brunn-Minkowski type". Proc...

type of duality relation. List of convexity topics John ellipsoid Brunn–Minkowski theorem, which has many implications relevant to the geometry of convex...

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)...

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

{\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...

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

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 ≥...

isoperimetric inequality. The Brunn–Minkowski inequality also leads to Anderson's theorem in statistics. The proof of the Brunn–Minkowski inequality predates modern...

minimization Fenchel's duality theorem Geometry Convex geometry Brunn–Minkowski theorem Differential geometry Fenchel's theorem Hyperbolic geometry Jakob Nielsen...

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...

inequality closely related to the reverse Young's inequality, the Brunn–Minkowski inequality and a number of other important and classical inequalities...

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...

1016/0022-0531(77)90095-3 Schneider, Rolf (1993), Convex Bodies: The Brunn–Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44,...

Numerous geometric inequalities, such as the Brunn–Minkowski inequality for convex bodies and Minkowski's first inequality, are special cases of the Alexandrov–Fenchel...

"Zonoids and other classes of convex bodies" in Convex bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993. Shephard, G. C...

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...

Lusternik–Schnirelmann category Lyusternik's generalization of the Brunn–Minkowski theorem Pavel Alexandrov et al., LAZAR' ARONOVICH LYUSTERNIK (on the occasion...

Convex Bodies: the Brunn-Minkowski Theory, Cambridge: Cambridge University Press Nirenberg, L. (1953). "The Weyl and Minkowski problems in differential...

(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...

location missing publisher (link) Gardner, Richard J. (2002). "The Brunn–Minkowski inequality". Bull. Amer. Math. Soc. (N.S.). 39 (3): 355–405 (electronic)...