Open Access
January 2015 Convexity estimates for surfaces moving by curvature functions
Ben Andrews, Mat Langford, James McCoy
J. Differential Geom. 99(1): 47-75 (January 2015). DOI: 10.4310/jdg/1418345537


We consider the evolution of compact surfaces by fully nonlinear, parabolic curvature flows for which the normal speed is given by a smooth, degree one homogeneous function of the principal curvatures of the evolving surface. Under no further restrictions on the speed function, we prove that initial surfaces on which the speed is positive become weakly convex at a singularity of the flow. This generalises the corresponding result of Huisken and Sinestrari for the mean curvature flow to the largest possible class of degree one homogeneous surface flows.


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Ben Andrews. Mat Langford. James McCoy. "Convexity estimates for surfaces moving by curvature functions." J. Differential Geom. 99 (1) 47 - 75, January 2015.


Published: January 2015
First available in Project Euclid: 12 December 2014

zbMATH: 1310.53057
MathSciNet: MR3299822
Digital Object Identifier: 10.4310/jdg/1418345537

Rights: Copyright © 2015 Lehigh University

Vol.99 • No. 1 • January 2015
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