Intermediate surface area measures and projection functions of convex bodies
It is proved that a convex polytopye in \(\mathbb{R}^ d\), whose faces satisfy a certain assumption of general position, is uniquely determined, up to translation or reflection, by its \(i\)th projection function if \(i\in \{2,\dots d-2\}\). For this, convex bodies in \(\mathbb{R}^ d\) whose \(i\)th area measure, \(i\in \{2,\dots, d-2\}\) is dominated by the sum of the \(i\)th area measures of two polytopes are investigated first. Also corresponding results for most convex bodies in terms of Baire category are studied.
scientific article; zbMATH DE number 734525