Singularity Profile in the Mean Curvature Flow

2009/02/13 by Sheng, Weimin, Wang, Xu-Jia · 3 citations
#35K55 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0902.2261

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 \Rⁿ⁺¹ with positive mean curvature is κ-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.

Cited by

• The Bounded Diameter Conjecture and Sharp Geometric Estimates for Mean Curvature Flow
• Mean curvature flow through singularities
• Noncollapsing for Curvature Flows with Inhomogeneous Speeds

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