Geodesic diameter of bodies of constant width
type: Item
instance of: scholarly article
title: Geodesic diameter of bodies of constant width
zbMATH Open document ID: 1187.52011
published in: Journal of Mathematical Sciences (New York)
publication date: 2010-01-19T00:00:00Z
review text: Let \(\Phi\) be a three-dimensional body of constant width \(B\). The geodesic diameter \(G\) of the surface of \(\Phi\) is estimated via \(B\) from above and from below. The main result states that the inequality \(G\leq \frac{\pi}{2} B\) holds, moreover the equality \(G= \frac{\pi}{2} B\) occurs if and only if \(\Phi\) is a body of revolution. The question is what is the optimal estimate from below for \(G\) in terms of \(B\). What is an extremal body, which has the minimal geodesic diameter \(G\) between all the convex bodies of a fixed constant width \(B\)?
reviewed by: Anatoliy Milka
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 5660128
zbMATH Keywords: body of constant width
zbMATH Keywords: geodesic diameter
author: Victor A. Zalgaller
MaRDI profile type: Publication
full work available at URL: s10958-009-9561-5
OpenAlex ID: W2088857126
cites work: Q4753788
DOI: 10.1007/S10958-009-9561-5
description: scientific article; zbMATH DE number 5660128