Starshaped hypersurfaces and the mean curvature flow
type: Item
instance of: scholarly article
title: Starshaped hypersurfaces and the mean curvature flow
zbMATH Open document ID: 0903.53039
author: Knut Smoczyk
published in: Manuscripta Mathematica
publication date: 1998-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/156372
review text: The author generalizes a result of \textit{G. Huisken} and \textit{C. Sinestrari} [`Mean curvature flow singularities for mean convex surfaces', Calc. Var. Partial Differ. Equ. 8, No.1, 1-14 (1999)], giving conditions such that under the mean curvature flow a type II singularity develops. Whereas Huisken-Sinestrari's paper gets the result assuming that the compact initial hypersurface is mean convex, the present paper poses a priori estimates on a whole family of closed hypersurfaces evolving by mean curvature. The proof uses essentially the same methods as Huisken-Sinestrari's paper. The second part of the paper shows that the a priori estimates are satisfied for mean convex hypersurfaces and some variety hereof and for starshaped hypersurfaces.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1151665
zbMATH Keywords: mean curvature flow
zbMATH Keywords: mean convex hypersurfaces
zbMATH Keywords: starshaped hypersurfaces
reviewed by: Barbara Priwitzer
MaRDI profile type: Publication
OpenAlex ID: W2040364864
DOI: 10.1007/S002290050025
description: scientific article; zbMATH DE number 1151665