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Stability estimates for star bodies in terms of their intersection bodies

Mathematika, 1998
Let \({\mathcal S}_c\) denote the class of star bodies in \(\mathbb{R}^d\) which are centrally symmetric with respect to the origin. The intersection body \(IK\) of \(K\in{\mathcal S}_c\) is the star body with radial function given by \(\rho_{IK} (u)=V_{d-1} (K\cap u^\perp)\) for unit vectors \(u\) (here \(V_{d-1}\) is the \((d-1)\)-dimensional volume).
Stefano Campi
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Lipschitz Star Bodies

Acta Mathematica Scientia, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Youjiang Lin, Yuchi Wu
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The Orlicz–Lorentz centroid inequality for star bodies*

Monatshefte Fur Mathematik, 2022
The paper is inspired by the work [\textit{V. H. Nguyen}, Adv. Appl. Math. 92, 99--121 (2018; Zbl 1380.52011)] on Orlicz-Lorentz centroid bodies. The author extends the Orlicz-Lorentz Busemann-Petty centroid inequality for convex bodies due to Nguyen to the more general case of star bodies.
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Metrics in the family of star bodies

Advances in Geometry, 2013
Abstract In this paper we consider different ways of introducing metrics in the family of star bodies. We begin with basic properties of metrics commonly used. Then we use selectors (see Definition 4.1) to extend the radial metric (see Definition 3.2) over the class of all star bodies in n-dimensional euclidean space. This way we obtain
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Radial continuous rotation invariant valuations on star bodies

Advances in Mathematics, 2016
We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=∫Sn−1θ(ρK)dm,
Ignacio Villanueva
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Radial continuous valuations on star bodies

Journal of Mathematical Analysis and Applications, 2017
We show that a radial continuous valuation defined on the n-dimensional star bodies extends uniquely to a continuous valuation on the n-dimensional bounded star sets.
Pedro Tradacete, Ignacio Villanueva
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L p -mixed intersection bodies and star duality [PDF]

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2010
The paper extends the two notions of the dual mixed volumes and L p-intersection body to q-dual mixed volumes and L p-mixed intersection body, respectively. Inequalities for the star dual of L p-mixed intersection bodies are established. © Indian Academy
Wing-Sum Cheung, Zhao Chang-Jian, Cheung Wing-Sum   +2 more
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Star Bodies and Diophantine Approximation

Journal of the London Mathematical Society, 1991
Let \(F\) be the distance function of a star body \(S=\{x\in\mathbb{R}^ n: F(x)\max\{\beta_ i\}=\beta\)). The exact value is then \(\dim W=n- 1+2\beta/(\tau+\beta)\). As the author remarks, the ideas of the proof can be applied to extend related earlier work on rational Diophantine approximation [see e.g. \textit{Yu Kunrui}, J. Lond. Math.
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Looking for Selectors of Star Bodies

Geometriae Dedicata, 2000
Following the line of previous papers, the author studies the possibilities of choosing ``good'' points inside a convex body or a star set. More precisely, let \({\mathcal F}\) be a family of star sets in \(\mathbb{R}^n\), a function \(s:{\mathcal F}\to \mathbb{R}^n\) is a selector for \({\mathcal F}\) if \(s(A)\in \text{ker} A\), where \(\text{ker} A\)
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Star Bodies/Freak Bodies/Women's Bodies

Media International Australia, 2008
An exploration of the contexts surrounding images of female celebrities in Australian weekly women's magazines complicates any simple cause-and-effect relationship between women's behaviour and celebrity glamour by revealing parallels between the construction of star personae and the discourses surrounding the display of sideshow ‘freaks’.
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