Rectangular convexity of convex domains of constant width
type: Item
instance of: scholarly article
title: Rectangular convexity of convex domains of constant width
zbMATH Open document ID: 0694.52001
DOI: 10.1007/BF00150684
author: Károly jun. Böröczky
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: A set M in the plane is called rectangular convex (r-convex) if, for any two distinct points x, y in M, there exists a rectangle R in M that contains x and y. \textit{R. Blind}, \textit{G. Valette} and \textit{T. Zamfirescu} [ibid. 9, 317-327 (1980; Zbl 0436.52007)] proved that, if M is compact, centrally symmetric, all its extreme points lie on a circle, and it has an inner point in the plane topology, then M is r-convex. They conjecture that these are the only compact r-convex sets. To support this conjecture the author proves in this paper that a closed convex domain of constant width must be a circle if it is assumed to be r-convex.
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 4136876
zbMATH Keywords: rectangular convexity
zbMATH Keywords: convex domain of constant width
zbMATH Keywords: circle
reviewed by: Bernd Wegner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00150684
OpenAlex ID: W2995648829
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description: scientific article; zbMATH DE number 4136876