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Cylindrical estimates for hypersurfaces moving by convex curvature functions

Andrews, Ben; Langford, Mat


We prove a complete family of `cylindrical estimates' for solutions of a class of fully non-linear curvature flows, generalising the cylindrical estimate of Huisken-Sinestrari [HS09, Section 5] for the mean curvature flow. More precisely, we show that, for the class of flows considered, an (m + 1)-convex (0 ≤ m ≤ n - 2) solution becomes either strictly m-convex, or its Weingarten map approaches that of a cylinder Rᵐ x Sⁿ⁻ ᵐ at points where the curvature is becoming large. This result...[Show more]

CollectionsANU Research Publications
Date published: 2014-09-27
Type: Journal article
Source: Analysis and PDE 7.5 (2014): 1091-1107
DOI: 10.2140/apde.2014.7.1091


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