An isoperimetric inequality with applications to curve shortening
type: Item
instance of: scholarly article
title: An isoperimetric inequality with applications to curve shortening
zbMATH Open document ID: 0534.52008
DOI: 10.1215/S0012-7094-83-05052-4
author: Michael E. Gage
published in: Duke Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: For closed convex \(C^ 2\) curves in the plane with length L, area A and curvature function \(\kappa\), the inequality \(\pi \frac{L}{A}\leq \int^{L}_{O}\kappa^ 2ds\) is proved. It is used to show the following: When a convex curve is deformed along its (inner) normal at a rate proportional to its curvature, then the isoperimetric ratio \(L^ 2/A\) decreases.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 3848142
zbMATH Keywords: convex curve
zbMATH Keywords: deformation of curves
zbMATH Keywords: length
zbMATH Keywords: area
zbMATH Keywords: curvature
zbMATH Keywords: isoperimetric ratio
Wikidata QID: Q57535356
reviewed by: Rolf Schneider
MaRDI profile type: Publication
cites work: Bonnesen-Style Isoperimetric Inequalities
full work available at URL: s0012-7094-83-05052-4
OpenAlex ID: W1484178435
description: scientific article; zbMATH DE number 3848142