Brunn-Minkowski inequality

By V. V. Buldygin, A. B. Kharazishvili. 2000

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View Paper: https://www.semanticscholar.org/paper/995feec94da76e2c686e9921a86cbe2076b37fc9

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In Applied Mathematics

Citations in the corpus

A Riemannian interpolation inequality à la Borell, Brascamp and Lieb (2001, result): “Applying this inequality to indicator functions of sets A, B ⊂ Rn one recovers, after suitable scaling, the Brunn-Minkowski inequality: vol1/n[(1− t)A+ tB] ≥ (1− t) vol 1/n A+ t vol1/n B. (1) First derived in connection with the isoperimetric theorem, applications of (1) pervade convex geometry; see”
Necessary subspace concentration conditions for the even dual Minkowski problem (2017, methodology): “ have equality in (2.1) for some 0 < λ < 1 if and only if K 0 and K 1 lie in parallel hyperplanes or they are homothetic, i.e., there exist a t ∈ Rn and µ ≥ 0 such that K 1 = t+µK 0 (see, e.g., [20], [48, Sect. 6.1]). 3. A Brunn-Minkowskitype inequalityformomentsof the Euclidean norm In this s”
An extension of Minkowski's theorem and its applications to questions about projections for measures (2016, methodology): “Firstly, if 1 r ≤ p, then the statement follows automatically by the standard inequality for q−averages Mq(λ, a, b) ≤Mq′(λ, a, b), whenever q ≤ q′ (see the definition (5) and Gardner [20] for more details).”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, background): “This inequality and its generalizations lie at the heart of the Brunn–Minkowski theory of convex sets, which is by now a classical object of study, having applications in a multitude of other fields [52, 21, 9, 20].”
The openness conjecture and complex Brunn-Minkowski inequalities (2014, positive): “THE BRUNN-M INKOWSKI THEOREM The classical Brunn-Minkowski theorem for convex bodies (s ee e g [12] for a nice account, including history and applications) can be formulated in th e following way.”
Solving convex programs by random walks (2004, neutral): “[Gardner 2002; Schneider 1993]).”
COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (2005, background): “See [7] for an excellent survey of this inequality and related ideas.”
Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport (2006, background): “From the beginning of the nineteen-seventies there has been a significant and systematic effort to obtain functional versions of geometric inequalities (see for instance [8, 9, 36] and the surveys [16, 18] for different points of view.”
Finsler interpolation inequalities (2009, background): “See [11, 15 ] for their correlation and historical background.”
Gaussian Brunn-Minkowski inequalities (2010, background): “No less than three recent surveys cover its extensive generalizations, variations, connections, and applications in probability and statistics, information theory, Banach space theory, algebraic geometry, geometric tomography, interacting gases, and crystallography; see [1], [14], and [28].”
Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary (2013, background): “ (∂M,g|∂M,exp(−V)dVol∂M) satisﬁes the CD(ρ0,N−1) condition for an appropriate ρ0. 1.3 Connections to the Brunn–Minkowski Theory Recall that the classical Brunn–Minkowski inequality in Euclidean space [59, 21] asserts that: Vol((1 −t)K+tL)1/n ≥ (1 −t)Vol(K)1/n +tVol(L)1/n , ∀t∈ [0,1] , (1.4) 7 for al”
Entropy and isoperimetry for linear and non-linear group actions (2008, background): “This is usually stated in the (equivalent) Hölder form (see [12] and references therein).”