Controlling curvature in Minkowski planes
type: Item
instance of: scholarly article
title: Controlling curvature in Minkowski planes
zbMATH Open document ID: 1008.53003
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-03-28T00:00:00Z
review text: The following variational problem was solved by \textit{H. H. Johnson} [Proc. Am. Math Soc. 44, 432-435 (1974; Zbl 0295.53001)]: To find, in the Euclidean plane, the curve of minimal length among all curves that join two given points with given tangents at these points and whose curvature is everywhere bounded above by a given constant. Here the author considers the analogous problem in a Minkowski plane (\(=2\)-dimensional flat Finsler space), i.e., in the case that length and curvature are measured with respect to a non-Euclidean norm.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 49Q10
zbMATH DE Number: 1563102
zbMATH Keywords: bounded curvature
zbMATH Keywords: curve of minimal length
zbMATH Keywords: Minkowski plane
author: Mostafa Ghandehari
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7184
OpenAlex ID: W2019130771
cites work: Q5662999
cites work: The foundations of Minkowskian geometry
cites work: A Geometric Inequality for Plane Curves with Restricted Curvature
cites work: Q4402191
cites work: An Application of the Maximum Principle to the Geometry of Plane Curves
cites work: Q4716272
DOI: 10.1006/JMAA.2000.7184
description: scientific article; zbMATH DE number 1563102