Reduced strictly convex plane figure is of constant width
type: Item
instance of: scholarly article
title: Reduced strictly convex plane figure is of constant width
zbMATH Open document ID: 0586.52002
DOI: 10.1007/BF01221008
published in: Journal of Geometry
publication date: 1986-01-01T00:00:00Z
review text: A convex body \(K\subset R^ d\) is called reduced if for each convex body K'\(\subset K (K'\neq K)\) the width of K' is less than the width of K. In 1978 W. Heil posed the problem if each strictly convex reduced body is of constant width. For reduced convex bodies with smooth boundary this was proved by \textit{H. Groemer} [Monatsh. Math. 96, 29-39 (1983; Zbl 0513.52003)]. The author proves Heil's problem for \(d=2\). A solution of Heil's problem for all d is announced by \textit{J. Böhm} [Diskrete Geometrie, 3. Kolloq., Salzburg 1985, 49-51 (1985; Zbl 0587.52001)].
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 3940132
zbMATH Keywords: minimal width
zbMATH Keywords: reduced convex bodies
author: B. V. Dekster
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Q4753788
cites work: Extremal convex sets
description: scientific article; zbMATH DE number 3940132