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# Cylindrical estimates for hypersurfaces moving by convex curvature functions

Type of Publication: | Journal article |

Author: | Andrews, Ben; Langford, Mat |

Year of publication: | 2014 |

Published in: | Analysis & PDE ; 7 (2014), 5. - pp. 1091-1107. - ISSN 2157-5045. - eISSN 1948-206X |

DOI (citable link): | https://dx.doi.org/10.2140/apde.2014.7.1091 |

Summary: |
We prove a complete family of cylindrical estimates for solutions of a class of fully nonlinear curvature flows, generalising the cylindrical estimate of Huisken and Sinestrari [Invent. Math. 175:1 (2009), 1–14, §5] for the mean curvature flow. More precisely, we show, for the class of flows considered, that, at points where the curvature is becoming large, an (m+1)-convex (0≤m≤n−2) solution either becomes strictly m-convex or its Weingarten map becomes that of a cylinder R
^{m}×S^{n−m}. This result complements the convexity estimate we proved with McCoy [Anal. PDE 7:2 (2014), 407–433] for the same class of flows. |

Subject (DDC): | 510 Mathematics |

Keywords: | curvature flows, cylindrical estimates, fully nonlinear, convexity estimates |

Bibliography of Konstanz: | Yes |

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ANDREWS, Ben, Mat LANGFORD, 2014. *Cylindrical estimates for hypersurfaces moving by convex curvature functions*. In: Analysis & PDE. **7**(5), pp. 1091-1107. ISSN 2157-5045. eISSN 1948-206X. Available under: doi: 10.2140/apde.2014.7.1091

@article{Andrews2014Cylin-30117, title={Cylindrical estimates for hypersurfaces moving by convex curvature functions}, year={2014}, doi={10.2140/apde.2014.7.1091}, number={5}, volume={7}, issn={2157-5045}, journal={Analysis & PDE}, pages={1091--1107}, author={Andrews, Ben and Langford, Mat} }