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

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Bourni T., Langford M.

Geometric Flows

2017

tom 2

nr 1

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. As a particular application, we prove an analogous result for a class of flows of embedded hypersurfaces which includes the flow of twoconvex hypersurfaces by the two-harmonic mean curvature.

Ograniczanie wyników

1 Geometric Flows

1 Bourni T.

1 Langford M.

1 2016

Wyniki wyszukiwania

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