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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
Affiliation:
Department of Geometry, Roland Eötvös University, Budapest, Pázmány Péter sétány 1/C, H-1117, Hungary e-mail: [email protected]
Károly J. Böröczky
Affiliation:
Alfréd Rényi Institute of Mathematics, PO Box 127, H-1364, Budapest Hungary e-mail: [email protected]
Carsten Schütt
Affiliation:
Mathematisches Seminar, Christian Albrechts Universität, 24098 Kiel, Germany e-mail: [email protected]
Gergely Wintsche
Affiliation:
Teacher Training Department, Roland Eötvös University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2008

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