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The Brunn-Minkowski Inequality and Related Results

, 2018
Trista A Mullin
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Brunn-Minkowski type inequality for product measures and unconditional convex bodies

, 2015
Piotr Nayar, Artem Zvavitch
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Brunn-Minkowski inequality

, 2000
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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Companions to the Brunn–Minkowski inequality

Positivity
Let \(\mathcal{C}\) be the family of all compact convex sets in \(\mathbb{R}^n\). For \(A, B \in \mathcal{C}\) denote by \(\operatorname{Vol}(A)\) the Lebesque measure of \(A\) and by \(\Delta (A,B) = \big[\operatorname{Vol}(A)\big]^{1/n} + \big[\operatorname{Vol}(B)\big]^{1/n} - \big[\operatorname{Vol}(A + B)\big]^{1/n}\). An \((m + 1)\)-tuple \((B_0,
Marek Niezgoda
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Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-Brunn–Minkowski inequality for projection bodies

Acta Mathematica Hungarica
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W. Wang
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The functional Orlicz–Brunn–Minkowski inequality for q‐torsional rigidity

Mathematika, 2023
In this paper, we obtain the functional Orlicz–Brunn–Minkowski inequality and the functional Orlicz–Minkowski inequality for q‐torsional rigidity in the smooth category.
Jin-Yan Hu, Pingyuan Zhang
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The Dual $$\phi $$-Brunn–Minkowski Inequality

Mediterranean Journal of Mathematics, 2021
Let \(K, L\subset\mathbb{R}^n\) be star bodies (i.e., star-shaped sets with respect to the origin, having continuous radial function), and let \(\rho_K\) and \(\rho_L\) be the radial functions of \(K\) and \(L\), respectively. Let \(\phi\in C^1((0,\infty))\) be strictly decreasing and concave, and assume that \(\log\circ\phi^{-1}\) is a convex function.
Shi, Wei, Li, Tian, Wang, Weidong
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Stability of the Logarithmic Brunn–Minkowski Inequality in the Case of Many Hyperplane Symmetries

Studia scientiarum mathematicarum Hungarica (Print), 2021
In the case of symmetries with respect to 𝑛 independent linear hyperplanes, a stability versions of the Logarithmic Brunn–Minkowski Inequality and the Logarithmic Minkowski Inequality for convex bodies are established.
K. Boroczky, A. De
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On Discrete LOG-Brunn--Minkowski Type Inequalities

SIAM Journal on Discrete Mathematics, 2022
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Hernández Cifre, María A., Lucas, Eduardo   +1 more
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A Brunn–Minkowski-Type Inequality

Geometriae Dedicata, 1999
For convex bodies \(K,L\) in \(\mathbb{R}^n\), let \(M(K,L): =\max_{x\in \mathbb{R}^n}|K\cap(x+L)|\) (where \(|\cdot|\) denotes volume). The author conjectures that \[ |K+L |^{1/n}\geq M(K,L)^{1/n} +{|K |^{1/n} |L|^{1/n}\over M(K,L)^{1/n}}, \] which would be a useful improvement of the Brunn-Minkowski theorem.
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