Mathematical Proceedings of the Cambridge Philosophical Society

Determination of a convex body from the average of projections and stability results

a1 Department of Mathematics, University of Dallas, Irving, Texas 75062 USA; e-mail:


Analysis of projections of a convex body is a familiar topic in tomography. However, instead of considering standard projection bodies, this work investigates a convex body introduced by Schneider [8] which is a Minkowski average of projections. The question addressed here is similar to that posed by Goodey and Weil [4] with respect to Minkowski averages of sections, as opposed to projections, that is, can the shape of a convex body be determined from random sections? Their main result shows that a body K is determined by the average of its two-dimensional sections, but not by the average of its one-dimensional sections. The goal of this study is to uncover the extent to which a convex body is determined by the average of its projections.

(Received February 14 1996)
(Revised January 2 1997)