Minimal ellipsoids and their duals
type: Item
instance of: scholarly article
title: Minimal ellipsoids and their duals
zbMATH Open document ID: 0673.52002
DOI: 10.1007/BF02844267
publication date: 1988-01-01T00:00:00Z
review text: It is proved that most (in certain sense) convex bodies in the euclidean d-space \(E^ d\) touch the boundaries of their minimal circumscribed and maximal inscribed ellipsoids in precisely \(d(d+3)/2\) points. Related results on compact sets in \(E^ d\) are contained in the paper, too. [Cf. the author, Discrete Geometry and convexity, Ann. N. Y. Acad. Sci. 440, 163-170 (1985; Zbl 0571.52007) and \textit{T. Zamfirescu}, J. Reine Angew. Math. 350, 183-187 (1984; Zbl 0557.52004)].
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 4101989
zbMATH Keywords: convex bodies
zbMATH Keywords: euclidean d-space
zbMATH Keywords: minimal circumscribed
zbMATH Keywords: maximal inscribed ellipsoids
zbMATH Keywords: compact sets
author: Peter M. Gruber
reviewed by: Ernest Jucovič
MaRDI profile type: Publication
cites work: Über die kleinste umbeschriebene und die grösste einbeschriebene Ellipse eines konvexen Bereichs
cites work: Q4098301
cites work: Q5556250
cites work: Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden
cites work: Some applications of means of convex bodies
cites work: Stability of Isometries
cites work: Q3689014
cites work: Q4104377
cites work: The geometry of normed spaces
cites work: Q5534404
cites work: Q3050157
cites work: The Equivalence of Two Extremum Problems
cites work: On Khachian's algorithm and minimal ellipsoids
cites work: Dual optimization problems in stochastics
cites work: Q5514233
cites work: Q3215459
cites work: Q5603915
cites work: Q5603731
cites work: Geometric approaches to design of experiment
cites work: Points of infinitely many normals to convex surfaces.
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4101989