Contents Online
Methods and Applications of Analysis
Volume 16 (2009)
Number 2
Singularity Profile in the Mean Curvature Flow
Pages: 139 – 156
DOI: https://dx.doi.org/10.4310/MAA.2009.v16.n2.a1
Authors
Abstract
In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space $Bbb R^n+1$ with positive mean curvature is $kappa$-noncollapsing, and a blow-up sequence converges locally smoothly along a subsequence to a smooth, convex blow-up solution. As a consequence we obtain a local Harnack inequality for the mean convex flow.
Keywords
Mean curvature flow, singularity profile, $kappa$-noncollapsing
2010 Mathematics Subject Classification
35K55, 53C44
Published 1 January 2009