Volume 16, issue 3 (2012)
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
Noncollapsing in mean-convex mean curvature flow

Ben Andrews
Geometry & Topology 16 (2012) 1413–1418
DOI: 10.2140/gt.2012.16.1413
Abstract

We provide a direct proof of a noncollapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence.

Keywords
mean curvature flow, noncollapsing
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 58J35, 35K93
References
Publication
Received: 31 July 2011
Revised: 30 January 2012
Accepted: 23 May 2012
Published: 24 July 2012
Proposed: Tobias H Colding
Seconded: John Lott, Gang Tian
Authors
Ben Andrews
Mathematical Sciences Institute
Australian National University
ACT 0200
Australia
http://www.maths.anu.edu.au/~andrews/