Volume 24, issue 2 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Closed ideal planar curves

Ben Andrews, James McCoy, Glen Wheeler and Valentina-Mira Wheeler

Geometry & Topology 24 (2020) 1019–1049
Abstract

We use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the L2 sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiply covered circle. Moreover, we show that curves in any homotopy class with initially small L3ks22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.

PDF Access Denied

We have not been able to recognize your IP address 18.97.14.90 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
constant mean curvature, curvature flow, geometric evolution equation
Mathematical Subject Classification 2010
Primary: 35K25, 53C44
Secondary: 58J35
References
Publication
Received: 14 October 2018
Revised: 17 July 2019
Accepted: 17 August 2019
Published: 23 September 2020
Proposed: Tobias H Colding
Seconded: Bruce Kleiner, John Lott
Authors
Ben Andrews
Applied and Nonlinear Analysis Group
Mathematical Sciences Institute
Australian National University
Canberra, ACT
Australia
James McCoy
Priority Research Centre for Computer-Assisted Research Mathematics and its Applications
School of Mathematical & Physical Sciences
University of Newcastle
Callaghan, NSW
Australia
Glen Wheeler
Institute for Mathematics and its Applications
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong, NSW
Australia
Valentina-Mira Wheeler
Institute for Mathematics and its Applications
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong, NSW
Australia