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MATHEMATICA SCANDINAVICA, 1990 There are several ways to generalize the classical concept of affine surface area of a sufficiently smooth convex body \(K\) in \(\mathbb{R}^ n\) due to Blaschke to arbitrary convex bodies [see \textit{K. Leichtweiss}, Manuscr. Math. 56, 429-464 (1986; Zbl 0588.52011), \textit{E. Lutwak}, Adv. Math. 85, No. 1, 39-68 (1991; Zbl 0727.53016) and \textit{C.
Werner, Elisabeth, Schütt, Carsten
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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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Competitively Chasing Convex Bodies [PDF]
SIAM Journal on Computing, 2019 Let $\mathcal{F}$ be a family of sets in some metric space. In the $\mathcal{F}$-chasing problem, an online algorithm observes a request sequence of sets in $\mathcal{F}$ and responds (online) by giving a sequence of points in these sets. The movement cost is the distance between consecutive such points.
Sébastien Bubeck +3 more
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The maximum relative diameter for multi-rotationally symmetric planar convex bodies [PDF]
, 2016 In this work we study the maximum relative diameter functional dM in the class of multi-rotationally symmetric planar convex bodies. A given set C of this class is k-rotationally symmetric for k 2 {k1, . . . , kn} N, and so it is natural to consider
Cañete Martín, Antonio Jesús
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Lattice reduced and complete convex bodies [PDF]
The purpose of this paper is to study convex bodies (Formula presented.) for which there exists no convex body (Formula presented.) of the same lattice width.
Freyer, Ansgar +1 more
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Some new Brunn-Minkowski-type inequalities in convex bodies
International Journal of Mathematics and Mathematical Sciences, 2005 We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.
Zhao Chang-Jian +2 more
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On Some Results in the Geometry of Convex Bodies and their Applications
Моделирование и анализ информационных систем, 2015 We give a survey of some results in the geometry of convex bodies and their applications.
M. V. Nevskii
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Shadows of Convex Bodies [PDF]
Transactions of the American Mathematical Society, 1991 It is proved that if C C is a convex body in
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General Blaschke Bodies and the Asymmetric Negative Solutions of Shephard Problem
Mathematics, 2019 In this article, based on the Blaschke combination of convex bodies, we define the general Blaschke bodies and obtain the extremal values of their volume and affine surface area. Further, we study the asymmetric negative solutions of the Shephard problem
Tian Li, Weidong Wang, Yaping Mao
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Forum of Mathematics, SigmaA spectral convex set is a collection of symmetric matrices whose range of eigenvalues forms a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal–Sottile–Sturmfels (2011). We study this class of convex bodies,
Raman Sanyal, James Saunderson
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