Singularity Profile in the Mean Curvature Flow
Sheng, Weimin ; Wang, Xu-Jia
Methods Appl. Anal., Tome 16 (2009) no. 1, p. 139-156 / Harvested from Project Euclid
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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.
Publié le : 2009-06-15
Classification:  Mean curvature flow,  singularity profile,  $kappa$-noncollapsing,  53C44,  35K55 
@article{1257170933,
     author = {Sheng, Weimin and Wang, Xu-Jia},
     title = {Singularity Profile in the Mean Curvature Flow},
     journal = {Methods Appl. Anal.},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 139-156},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257170933}
}

Sheng, Weimin; Wang, Xu-Jia. Singularity Profile in the Mean Curvature Flow. Methods Appl. Anal., Tome 16 (2009) no. 1, pp.  139-156. http://gdmltest.u-ga.fr/item/1257170933/