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Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2008
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