Convexity and the average curvature of plane curves
type: Item
instance of: scholarly article
title: Convexity and the average curvature of plane curves
zbMATH Open document ID: 0887.53002
DOI: 10.1023/A:1004912521664
author: Jeffrey C. Lagarias
author: T. J. Richardson
published in: Geometriae Dedicata
publication date: 1998-05-25T00:00:00Z
review text: Let the average curvature \(M(\gamma)\) of a rectifiable closed curve \(\gamma\) in the Euclidean plane be its total absolute curvature divided by its length. The main result is: Let \(D\) be a compact convex set in the Euclidean plane with nonempty interior. If \(\gamma\) is any closed rectifiable curve contained in \(D\), then \((\partial D)\leq M(\gamma)\). This result improves inequalities given by I. Fáry, resp. L. A. Santaló.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 1059626
zbMATH Keywords: convexity
zbMATH Keywords: plane curve
zbMATH Keywords: geometric inequalities
zbMATH Keywords: total curvature
zbMATH Keywords: average curvature
reviewed by: Eberhard Teufel
MaRDI profile type: Publication
full work available at URL: a:1004912521664
OpenAlex ID: W1517451946
description: scientific article; zbMATH DE number 1059626