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June 2009 Singularity Profile in the Mean Curvature Flow
Weimin Sheng, Xu-Jia Wang
Methods Appl. Anal. 16(2): 139-156 (June 2009).


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.


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Weimin Sheng. Xu-Jia Wang. "Singularity Profile in the Mean Curvature Flow." Methods Appl. Anal. 16 (2) 139 - 156, June 2009.


Published: June 2009
First available in Project Euclid: 2 November 2009

zbMATH: 1184.53071
MathSciNet: MR2563745

Primary: 35K55 , 53C44

Keywords: $kappa$-noncollapsing , Mean curvature flow , singularity profile

Rights: Copyright © 2009 International Press of Boston

Vol.16 • No. 2 • June 2009
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