Canadian Mathematical Society
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

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

Open Access article
 Printed: Feb 2008
  • Károly Böröczky
  • Károly J. Böröczky
  • Carsten Schütt
  • Gergely Wintsche
Format:   HTML   LaTeX   MathJax   PDF   PostScript  


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

© Canadian Mathematical Society, 2017 :