Golubyatnikov, V. P. On unique reconstruction of convex and visible compacta by their projections. (Russian) Zbl 0738.52004 Mat. Sb. 182, No. 5, 611-621 (1991). This is a contribution to the question: What conditions imply that if two compacta have congruent projections on 2-dimensional flats, then the compacta are congruent? Here are two typical results of the paper.1. Suppose \(W_ 1\), \(W_ 2\) are simply connected compacta in \(\mathbb{R}^ n\) with the property that through each \(n-2-\ell\) dimensional plane which does not intersect \(W_ i\) there can be drawn an \(n-2\) dimensional plane which does not intersect \(W_ i\); here \(0<\ell\leq n-2\). If the projections of \(W_ 1\), \(W_ 2\) on any 2-dimensional plane are properly congruent and have no rotational symmetry in that plane, then \(W_ 1\), \(W_ 2\) can be made to coincide by a translation of central symmetry. 2. If \(V_ 1\), \(V_ 2\) are compact convex sets in \(\mathbb{R}^ 3\) whose projections on any plane are properly similar and have no rotational symmetry, then \(V_ 1\), \(V_ 2\) can be made to coincide by a homothety. Reviewer: W.J.Firey (Corvallis) Cited in 2 ReviewsCited in 2 Documents MSC: 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) 52A30 Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.) Keywords:congruent compacta; convex compacta; visible compacta; congruent projections PDFBibTeX XMLCite \textit{V. P. Golubyatnikov}, Mat. Sb. 182, No. 5, 611--621 (1991; Zbl 0738.52004) Full Text: EuDML