Results 61 to 70 of about 489,827 (153)
The Brunn-Minkowski inequality for random sets [PDF]
, 1990 The Brunn-Minkowski inequality asserts a concavity feature of the volume functional under convex addition of sets. Among its applications has been Anderson's treatment of multivariate densities.
Vitale, Richard A
core +1 more source
Subgroup Decomposition of the Gini Coefficient: A New Solution to an Old Problem
Econometrica, Volume 94, Issue 1, Page 169-192, January 2026.We derive a novel decomposition of the Gini coefficient into within‐ and between‐group inequality terms that sum to the aggregate Gini coefficient. This decomposition is derived from a set of axioms that ensure desirable behavior for the within‐ and between‐group inequality terms.
Vesa‐Matti Heikkuri, Matthias Schief
wiley +1 more source
Stability of inequalities in the dual Brunn-Minkowski theory [PDF]
, 1999 Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used.
Vassallo, Salvatore Flavio
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On Brunn–Minkowski-Type Inequalities for Polar Bodies
The Journal of Geometric Analysis, 2014 Let \( {\mathcal K}^{n}_0\) be the set of all convex bodies in \( {\mathbb R}^n \) containing the origin as an interior point. Given \( K, L \in {\mathcal K}^{n}_0 \), \( 1 \leq p \leq \infty \), and \( \lambda, \mu \geq 0 \), we denote by \( \lambda \cdot K +_p \, \mu \cdot L \) their Firey linear combination, its support function is defined by \[ h (\
Hernández Cifre, María de los Ángeles +1 more
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Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality [PDF]
Calculus of Variations and Partial Differential Equations, 2017 We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space.
Barchiesi Marco, Julin Vesa
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New fiber and graph combinations of convex bodies
Mathematika, Volume 71, Issue 4, October 2025.Abstract Three new combinations of convex bodies are introduced and studied: the Lp$L_p$ fiber, Lp$L_p$ chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways.
Steven Hoehner, Sudan Xing
wiley +1 more source
The log-Brunn-Minkowski inequality and its local version
, 2020 The conjectured log-Brunn-Minkowski inequality has attracted much interest since its introduction by Böröczky, Lutwak, Yang and Zhang in 2012. In this talk, I shall survey the connections between this inequality and various outstanding problems in ...
Putterman, Eli
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Lp Radial Blaschke-Minkowski Homomorphisms and Lp Dual Affine Surface Areas
Mathematics, 2019 Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered the Busemann-Petty problem for volume forms. Whereafter, Wang, Liu and He presented the L p radial Blaschke-Minkowski homomorphisms and extended Schuster ...
Zhonghuan Shen, Weidong Wang
doaj +1 more source
The sharp doubling threshold for approximate convexity
Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3229-3239, October 2024.Abstract We show for A,B⊂Rd$A,B\subset \mathbb {R}^d$ of equal volume and t∈(0,1/2]$t\in (0,1/2]$ that if |tA+(1−t)B|<(1+td)|A|$|tA+(1-t)B|< (1+t^d)|A|$, then (up to translation) |co(A∪B)|/|A|$|\operatorname{co}(A\cup B)|/|A|$ is bounded. This establishes the sharp threshold for the quantitative stability of the Brunn–Minkowski inequality recently ...
Peter van Hintum, Peter Keevash
wiley +1 more source
On discrete Brunn-Minkowski and isoperimetric type inequalities
Discrete Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iglesias López, David +2 more
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