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The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals [PDF]
Journal of Mathematical Analysis and Applications, 2000 Let \(K,L\) be convex bodies in Euclidean space \(\mathbb{E}^n\) with volumes \(V(K)=V(L)=1\), and let \(V_1(K,L)\) denote the mixed volume \(V(K, \dots, K,L)\). Then \[ V(K+L)^{1/n} -2\leq V_1(K,L) -1\leq {1\over n}\bigl(V(K+L)-2^n \bigr). \] These inequalities provide a quantitative improvement of the known equivalence of the Brunn-Minkowski ...
Vassallo, Salvatore Flavio +1 more
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The Brunn–Minkowski inequality for volume differences [PDF]
Advances in Applied Mathematics, 2004 Suppose that \(K\), \(L\), \(D\), \(D'\) are compact domains in \(\mathbb{R}^n\) such that \(D\) and \(D'\) are homothetic and convex and \(D\subset K\), \(D'\subset L\). It is proved (in a more general form) that for the volume \(V\) one has \[ ((V(K+ L)- V(D+ D'))^{1/n}\geq (V(K)- V(D))^{1/n}+ (V(L)- V(D'))^{1/n}.
Gangsong Leng
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The dual Brunn–Minkowski inequality for log-volume of star bodies
Journal of Inequalities and Applications, 2021 This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and the equivalent Minkowski inequality for mixed log-volume.
Dandan Lai, Hailin Jin
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On Isoperimetric Inequalities in Minkowski Spaces [PDF]
Journal of Inequalities and Applications, 2010 The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Horst Martini, Zokhrab Mustafaev
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A converse of Minkowski's inequality
Discrete Mathematics, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Horst Alzer, Stephan Ruscheweyh
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On Minkowski's inequality and its application
Journal of Inequalities and Applications, 2011 In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.
Cheung Wing-Sum, Zhao Chang-Jian
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The extremals of Minkowski’s quadratic inequality [PDF]
Duke Mathematical Journal, 2022 52 pages, 6 figures; final ...
Shenfeld, Yair, van Handel, Ramon
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Lp-dual three mixed quermassintegrals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-
Zhao Chang-Jian, Bencze Mihály
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Inequalities in Riemann–Lebesgue Integrability
Mathematics, 2023 In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality.
Anca Croitoru +3 more
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The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity [PDF]
Memoirs of the American Mathematical Society, 2021 In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, Cap
Akman, Murat +4 more
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