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Geometric Flows

Ed. by Carfora, Mauro / Mantegazza, Carlo

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2353-3382
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Type-II singularities of two-convex immersed mean curvature flow

Theodora Bourni / Mat Langford
Published Online: 2016-10-17 | DOI: https://doi.org/10.1515/geofl-2016-0001

Abstract

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.

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About the article

Received: 2016-05-09

Accepted: 2016-09-02

Published Online: 2016-10-17

Published in Print: 2016-10-01


Citation Information: Geometric Flows, Volume 2, Issue 1, Pages 1–17, ISSN (Online) 2353-3382, DOI: https://doi.org/10.1515/geofl-2016-0001.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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