Results 41 to 50 of about 489,757 (102)
Dual Brunn-Minkowski inequality for C-star bodies
, 2023 In this paper, we consider the concept of $C$-star body in a fixed pointed closed convex cone $C$ and study the dual mixed volume for $C$-star bodies. For $C$-star bodies, we establish the corresponding dual Brunn-Minkowski inequality, the dual Minkowski
Wang, Xudong, Xiang, Tingting
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The log-Brunn–Minkowski inequality [PDF]
, 2012 For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn–Minkowski inequality and a family of inequalities
Lutwak, Erwin +7 more
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Isoperimetric and Functional Inequalities
Моделирование и анализ информационных систем, 2018 We establish lower estimates for an integral functional$$\int\limits_\Omega f(u(x), \nabla u(x)) \, dx ,$$where \(\Omega\) -- a bounded domain in \(\mathbb{R}^n \; (n \geqslant 2)\), an integrand \(f(t,p) \, (t \in [0, \infty),\; p \in \mathbb{R}^n)\) --
Vladimir S. Klimov
doaj +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
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 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
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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 p-radial Blaschke and harmonic Blaschke additions
Journal of Inequalities and Applications, 2017 In the paper, we first improve the radial Blaschke and harmonic Blaschke additions and introduce the p-radial Blaschke and p-harmonic Blaschke additions.
Chang-Jian Zhao
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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
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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