Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells

Böröczky, Károly ; Böröczky, Károly J. ; Schütt, Carsten ; Wintsche, Gergely

Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 3-32

Résumé

Given $r\,>\,1$ , we consider convex bodies in ${{\mathbb{E}}^{n}}$ which contain a fixed unit ball, and whose extreme points are of distance at least $r$ from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As $r$ tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.

Détail

DOI : 10.4153/CJM-2008-001-x

Mots-clés : Primary, 52A27, secondary, 52A40

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