Analysis & PDE
- Anal. PDE
- Volume 7, Number 5 (2014), 1091-1107.
Cylindrical estimates for hypersurfaces moving by convex curvature functions
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 -convex () solution either becomes strictly -convex or its Weingarten map becomes that of a cylinder . This result complements the convexity estimate we proved with McCoy [Anal. PDE 7:2 (2014), 407–433] for the same class of flows.
Anal. PDE, Volume 7, Number 5 (2014), 1091-1107.
Received: 8 October 2013
Accepted: 30 June 2014
First available in Project Euclid: 20 December 2017
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Andrews, Ben; Langford, Mat. Cylindrical estimates for hypersurfaces moving by convex curvature functions. Anal. PDE 7 (2014), no. 5, 1091--1107. doi:10.2140/apde.2014.7.1091. https://projecteuclid.org/euclid.apde/1513731564