Swallowtail, Whitney umbrella and convex hulls
type: Item
instance of: scholarly article
title: Swallowtail, Whitney umbrella and convex hulls
zbMATH Open document ID: 1487.58035
published in: Journal of Dynamical and Control Systems
publication date: 2022-01-24T00:00:00Z
review text: The main result of the paper is the following: Consider a support hyperplane \(\pi\) of type \(A_1A_3\) to a smooth compact hypersurface \(M\) in \(\mathbb{R}^4\). Denote by \(P\) the type \(A_1\) endpoint of the support segment of \(\pi\). Let \(\Gamma\) be the boundary of the convex hull of the hypersurface \(M\). Then, any parallel projection of the germ at \(P\) of the singular point set of \(\Gamma\) to the hyperplane \(\pi\) for a generic \(M\) is diffeomorphic to the germ at zero of union of the cut swallowtail and the Whitney umbrella chamber (Theorem 1). This union is called by the author sailboat. Other author's paper directly connected to this topic are [\textit{V. D. Sedykh}, Funct. Anal. Appl. 11, 72--73 (1977; Zbl 0369.58009); Math. USSR, Sb. 47, 223--236 (1984; Zbl 0521.58008); Math. USSR, Sb. 63, No. 2, 499--505 (1989; Zbl 0679.58005); translation from Mat. Sb., Nov. Ser. 135(177), No. 4, 514--519 (1988); The sewing of the swallowtail and the Whitney umbrella in a four-dimensional control system. Moscow: Trudy GANG imeni I.M.Gubkina. 58--68 (1997); Izv. Math. 76, No. 2, 375--418 (2012; Zbl 1251.57021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 76, No. 2, 171--214 (2012)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 58K30
zbMATH DE Number: 7462062
zbMATH Keywords: convex hull
zbMATH Keywords: singularities
zbMATH Keywords: swallowtail
zbMATH Keywords: Whitney umbrella
author: V. D. Sedykh
MaRDI profile type: Publication
full work available at URL: s10883-020-09510-5
OpenAlex ID: W3080254097
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DOI: 10.1007/S10883-020-09510-5
description: scientific article; zbMATH DE number 7462062