Starshaped hypersurfaces and the mean curvature flow.

Knut Smoczyk

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Type-II singularities of two-convex immersed mean curvature flow

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We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations....

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We investigate curvature properties of hypersurfaces in semi-Riemannian spaces of constant curvature with the minimal polynomial of the second fundamental tensor of second degree. We present suitable examples of hypersurfaces.