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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

Károly Böröczky ,
Károly J. Böröczky ,
Carsten Schütt  and
Gergely Wintsche
Károly Böröczky
Affiliation:
Department of Geometry, Roland Eötvös University, Budapest, Pázmány Péter sétány 1/C, H-1117, Hungary e-mail: boroczky@cs.elte.hu
Károly J. Böröczky
Affiliation:
Alfréd Rényi Institute of Mathematics, PO Box 127, H-1364, Budapest Hungary e-mail: carlos@renyi.hu
Carsten Schütt
Affiliation:
Mathematisches Seminar, Christian Albrechts Universität, 24098 Kiel, Germany e-mail: schuett@math.uni-kiel.de
Gergely Wintsche
Affiliation:
Teacher Training Department, Roland Eötvös University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary e-mail: wgerg@ludens.elte.hu
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Abstract

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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.

Keywords

Primary52A27secondary52A40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 1 , 01 February 2008 , pp. 3 - 32
Copyright
Copyright © Canadian Mathematical Society 2008

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