Kiselman, Christer O. How smooth is the shadow of a smooth convex body? (English) Zbl 0601.52002 Serdica 12, 189-195 (1986). The author investigates the problem stated in the title of the paper. Let A be a convex compact body in \({\mathbb{R}}^ 3\) and \(P: {\mathbb{R}}^ 3\to {\mathbb{R}}^ 2\) a linear surjection. Then: 1) if \(\partial A\in C^ 1\), then \(\partial (P(A))\in C^ 1\); 2) if \(\partial A\in C^ 2\) with Lipschitz continuous second derivatives, then \(\partial (P(A))\) is twice differentiable; 3) if \(\partial A\) is real-analytic, then \(\partial (P(A))\in C^{2+\epsilon}\) for some \(\epsilon >0\). On the other hand, \(\partial A\in C^{\infty}\) does not imply \(\partial (P(A))\in C^ 2.\) Note that this paper is also published in J. Lond. Math. Soc. 33, 101-109 (1986). Reviewer: J.Danes Cited in 2 Documents MSC: 52A15 Convex sets in \(3\) dimensions (including convex surfaces) Keywords:smooth convex body; shadow PDFBibTeX XMLCite \textit{C. O. Kiselman}, Serdica 12, 189--195 (1986; Zbl 0601.52002)