Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# On Projection Bodies of Order One

Published:2009-09-01
Printed: Sep 2009
• Stefano Campi
• Paolo Gronchi
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

The projection body of order one $\Pi_1K$ of a convex body $K$ in $\R^n$ is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of $K$ onto hyperplanes through the origin. The paper contains an inequality for the support function of $\Pi_1K$, which implies in particular that such a function is strictly convex, unless $K$ has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order $n-1$.
 MSC Classifications: 52A40 - Inequalities and extremum problems

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2017 : https://cms.math.ca/