## Methods and Applications of Analysis

### Singularity Profile in the Mean Curvature Flow

#### 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.

#### Article information

Source
Methods Appl. Anal., Volume 16, Number 2 (2009), 139-156.

Dates
First available in Project Euclid: 2 November 2009