Starshaped hypersurfaces¶and the mean curvature flow
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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 , 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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