The normalized curve shortening flow and homothetic solutions
type: Item
instance of: scholarly article
title: The normalized curve shortening flow and homothetic solutions
zbMATH Open document ID: 0592.53002
author: Uwe Abresch
author: Joel C. Langer
published in: Journal of Differential Geometry
publication date: 1986-01-01T00:00:00Z
review text: The authors investigate the curve shortening flow; i.e. the evolution of a regular closed curve \(\gamma\) in the plane according to the equation \(\partial \gamma /\partial t=kN\) where k is the curvature and N the normal of \(\gamma\). First they modify the flow such that the curves maintain constant speed but are geometrically the same. Then they classify curves that evolve through homothetic curves. Furthermore they prove convergence and divergence results for the flow and compare these with the homothetic solutions.
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 3951450
zbMATH Keywords: curve shortening flow
zbMATH Keywords: closed curve
zbMATH Keywords: homothetic curves
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214440025
OpenAlex ID: W1482778848
Wikidata QID: Q57535283
DOI: 10.4310/JDG/1214440025
description: scientific article; zbMATH DE number 3951450