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INEQUALITIES BETWEEN MIXED VOLUMES OF CONVEX BODIES: VOLUME BOUNDS FOR THE MINKOWSKI SUM
Mathematika, Volume 66, Issue 4, Page 1003-1027, October 2020., 2020 Abstract In the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1+⋯+Pd of d‐dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,⋯,Pd).
Gennadiy Averkov +2 more
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On the stability of Brunn–Minkowski type inequalities
Journal of Functional Analysis, 2017 name ...
COLESANTI, ANDREA +2 more
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Generalizations of the Brunn–Minkowski inequality
Linear Algebra and its Applications, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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On Gaussian Brunn–Minkowski inequalities [PDF]
Studia Mathematica, 2009 In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also allows us to have semigroup proofs of the geometric Brascamp-Lieb inequality and of the reverse one
Franck Barthe, Nolwen Huet
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General L p $L_{p}$ -mixed chord integrals of star bodies
Journal of Inequalities and Applications, 2016 The notion of general mixed chord integrals of star bodies was introduced by Feng and Wang. In this paper, we extend the concept of the general mixed chord integrals to general L p $L_{p}$ -mixed chord integrals of star bodies.
Zhaofeng Li, Weidong Wang
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On the deterministic interior body of random polytopes
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract Let {Xi}i=1∞$\lbrace X_i\rbrace _{i=1}^{\infty }$ be a sequence of independent copies of a random vector X$X$ in Rn$\mathbb {R}^n$. We revisit the question to determine the asymptotic shape of the random polytope KN=conv{X1,…,XN}$K_N={\rm conv}\lbrace X_1,\ldots,X_N\rbrace$ where N>n$N>n$.
Minas Pafis, Natalia Tziotziou
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Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane
Discrete & Computational Geometry, 2019 For a set $A$ of points in the plane, not all collinear, we denote by ${\rm tr}(A)$ the number of triangles in any triangulation of $A$; that is, ${\rm tr}(A) = 2i+b-2$ where $b$ and $i$ are the numbers of points of $A$ in the boundary and the interior of $[A]$ (we use $[A]$ to denote "convex hull of $A$").
Böröczky, Károly J. +4 more
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Generalization of the Brunn–Minkowski Inequality in the Form of Hadwiger [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2016 A class of domain functionals has been built in the Euclidean space. The Brunn–Minkowski type of inequality has been applied to the said class and proved for it.
B.S. Timergaliev
doaj
Discrepancy of arithmetic progressions in boxes and convex bodies
Mathematika, Volume 72, Issue 2, April 2026.Abstract The combinatorial discrepancy of arithmetic progressions inside [N]:={1,…,N}$[N]:= \lbrace 1, \ldots, N\rbrace$ is the smallest integer D$D$ for which [N]$[N]$ can be colored with two colors so that any arithmetic progression in [N]$[N]$ contains at most D$D$ more elements from one color class than the other.
Lily Li, Aleksandar Nikolov
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