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The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity [PDF]
Memoirs of the American Mathematical Society, 2017 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 A
M. Akman +4 more
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Geometric approaches to establish the fundamentals of Lorentz spaces $\mathbb{R}_2^3$ and $\mathbb{R}_1^2$ [PDF]
Mathematica BohemicaThe aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space $\mathbb{R}_2^3$.
Sevilay Çoruh Şenocak, Salim Yüce
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Some logarithmic Minkowski inequalities for nonsymmetric convex bodies and related problems
Journal of Inequalities and Applications, 2020 In this paper, we show the existence of a solution to an even logarithmic Minkowski problem for p-capacity and prove some analogue inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies involving p-capacity.
Lewen Ji
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A Steiner Inequality for the Anisotropic Perimeter
Journal of Function Spaces, 2022 In this paper, we prove the monotonicity of the anisotropic perimeter of sets of finite perimeter under Steiner symmetrization by a variational formula of volume and an inequality for the anisotropic lower outer Minkowski content.
Jin Dai
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Orlicz hormonic Blaschke addition [PDF]
arXiv, 2021 Recently, Gardner, Hug and Weil have introduced the Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. Following this, in the paper we consider Orlicz dual Brunn-Minkowski theory. We introduce Orlicz hormonic Blaschke addition which is an extension of the Lp hormonic Blaschke addition and L p radial Minkowski addition ...
arxiv
Dual Brunn-Minkowski inequality for C-star bodies
AIMS MathematicsIn this paper, we introduced the concept of $ C $-star bodies in a fixed pointed closed convex cone $ C $ and studied the dual mixed volume for $ C $-star bodies.
Xudong Wang, Tingting Xiang
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Journal of Mathematics, 2022 By utilizing the peculiarities of superquadratic and subquadratic functions, we give the extensions for multidimensional inequalities of Hardy-type with general kernel.
M. Zakarya +4 more
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On Robust Global Error Bounds for a Class of Uncertain Piecewise Linear Inequality Systems
Axioms, 2022 This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets.
Wen Tan, Xiaole Guo, Xiangkai Sun
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Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane [PDF]
Discrete & Computational Geometry, 2018 For a set A of points in the plane, not all collinear, we denote by tr(A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
K. Böröczky +4 more
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Generalizations of Minkowski and Beckenbach–Dresher Inequalities and Functionals on Time Scales
International Journal of Analysis and Applications, 2020 We generalize integral forms of the Minkowski inequality and Beckenbach–Dresher inequality on time scales. Also, we investigate a converse of Minkowski’s inequality and several functionals arising from the Minkowski inequality and the Beckenbach–Dresher ...
Rabia Bibi +2 more
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