#### Vol. 7, No. 5, 2014

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Cylindrical estimates for hypersurfaces moving by convex curvature functions

### Ben Andrews and Mat Langford

Vol. 7 (2014), No. 5, 1091–1107
##### Abstract

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 $\left(m+1\right)$-convex ($0\le m\le n-2$) 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.

##### Keywords
curvature flows, cylindrical estimates, fully nonlinear, convexity estimates
##### Mathematical Subject Classification 2010
Primary: 53C44, 35K55, 58J35