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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Noncollapsing in mean-convex mean curvature flow

Ben Andrews

Geometry & Topology 16 (2012) 1413–1418
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/