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Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells |
Canad. J. Math. 60(2008), 3-32
Published:2008-02-01
Printed: Feb 2008
Printed: Feb 2008
- Károly Böröczky
- Károly J. Böröczky
- Carsten Schütt
- Gergely Wintsche
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 - Approximation by convex sets 52A40 - Inequalities and extremum problems |