Vol. 7, No. 5, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 (m+1)-convex (0 m n 2) solution either becomes strictly m-convex or its Weingarten map becomes that of a cylinder m × Snm. 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
Milestones
Received: 8 October 2013
Accepted: 30 June 2014
Published: 27 September 2014
Authors
Ben Andrews
Mathematical Sciences Institute
Australian National University
ACT 0200
Australia
Mathematical Sciences Center
Tsinghua University
Beijing 100084
China
Mat Langford
Mathematical Sciences Institute
Australian National University
ACT 0200
Australia
Fachbereich Mathematik und Statistik
Universität Konstanz
78457 Konstanz
Germany