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Starshaped hypersurfaces¶and the mean curvature flow


Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds that are close to them. This gives a classification of the possible singularities for these surfaces in the case n= 2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity occurs.

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Received: 6 June 1997 / Revised version: 24 October 1997

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Smoczyk, K. Starshaped hypersurfaces¶and the mean curvature flow . manuscripta math. 95, 225–236 (1998).

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  • Mathematics Subject Classification (1991): 53C42