Results 11 to 20 of about 32,897 (198)
The Orlicz Brunn–Minkowski inequality
Advances in Mathematics, 2014 The Orlicz-Brunn-Minkowski theory was introduced by Lutwak, Yang and Zhang, being an extension of the classical Brunn-Minkowski theory. It represents a generalization of the \(L_p\)-Brunn-Minkowski theory. For a convex, strictly increasing \(\phi:[0,\infty]\longrightarrow [0,\infty)\), with \(\phi(0)=0\) and \(K,L\) convex and compact sets containing ...
Xi, Dongmeng +2 more
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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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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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A nonabelian Brunn–Minkowski inequality
Geometric and Functional Analysis, 2023 AbstractHenstock and Macbeath asked in 1953 whether the Brunn–Minkowski inequality can be generalized to nonabelian locally compact groups; questions along the same line were also asked by Hrushovski, McCrudden, and Tao. We obtain here such an inequality and prove that it is sharp for helix-free locally compact groups, which includes real linear ...
Jing, Y, Tran, C-M, Zhang, R
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Boundary restricted Brunn–Minkowski inequalities
Communications in Contemporary Mathematics, 2023 In this paper, we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V. Milman regarding the volume of [Formula: see text] where [Formula: see text] and [Formula: see text] are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of ...
Shiri Artstein-Avidan +2 more
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On Dual Brunn-Minkowski Inequalities [PDF]
Mathematical Inequalities & Applications, 2005 On dual Brunn-Minkowski ...
Zhao, Changjian +2 more
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Lattice (List) Decoding Near Minkowski’s Inequality [PDF]
IEEE Transactions on Information Theory, 2022 14 pages, 2 ...
Ethan Mook, Chris Peikert
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The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals
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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Indagationes Mathematicae, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ChangJian, Z, Cheung, WS
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Minkowski Inequalities via Nonlinear Potential Theory [PDF]
Archive for Rational Mechanics and Analysis, 2022 AbstractIn this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n
Agostiniani V. +2 more
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