Singularities of convex hulls
type: Item
instance of: scholarly article
title: Singularities of convex hulls
zbMATH Open document ID: 0531.58013
DOI: 10.1007/BF00971558
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: [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.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3842807
zbMATH Keywords: germ of a convex hull
zbMATH Keywords: normal forms
zbMATH Keywords: functional module
author: V. D. Sedykh
MaRDI profile type: Publication
cites work: Q3915675
cites work: Gaussian distributions on locally compact abelian groups
cites work: Q4046802
description: scientific article; zbMATH DE number 3842807