Analysis & PDE

  • Anal. PDE
  • Volume 7, Number 5 (2014), 1091-1107.

Cylindrical estimates for hypersurfaces moving by convex curvature functions

Ben Andrews and Mat Langford

Full-text: Open access

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 (0mn2) 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.

Article information

Source
Anal. PDE, Volume 7, Number 5 (2014), 1091-1107.

Dates
Received: 8 October 2013
Accepted: 30 June 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731564

Digital Object Identifier
doi:10.2140/apde.2014.7.1091

Mathematical Reviews number (MathSciNet)
MR3265960

Zentralblatt MATH identifier
1312.53085

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 35K55: Nonlinear parabolic equations 58J35: Heat and other parabolic equation methods

Keywords
curvature flows cylindrical estimates fully nonlinear convexity estimates

Citation

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


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