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

  Published:2008-02-01
 Printed: Feb 2008
  • Károly Böröczky
  • Károly J. Böröczky
  • Carsten Schütt
  • Gergely Wintsche
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Abstract

Given $r>1$, we consider convex bodies in $\E^n$ 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.
MSC Classifications: 52A27, 52A40 show english descriptions Approximation by convex sets
Inequalities and extremum problems
52A27 - Approximation by convex sets
52A40 - Inequalities and extremum problems
 

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