Singularities of convex hulls
[See also the author's earlier paper, Mat. Sb., Nov. Ser. 119(161), No.2(10), 233-247 (1982; Zbl 0509.58005)]. Three theorems are proved and two hypotheses are conjectured. Theorem A. The singularity of the convex hull of the smooth compact k-manifold in \(R^ n\) has no module iff \(k=0\) or \(k=1\) and \(n-k=1\) or \(n-k=2\). Theorem B. If \(n-k>2\) then there exists a manifold and a singularity of its convex hull whose module contains indefinitely many functions in k variables. Hypothesis 1. For any \(n\geq 5\) there exists a manifold with \(co\dim =1\) or 2 and a singularity of its convex hull which has a functional module.
scientific article; zbMATH DE number 3842807