Journal of Differential Geometry

Convexity estimates for surfaces moving by curvature functions

Ben Andrews, Mat Langford, and James McCoy

Full-text: Open access


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.

Article information

J. Differential Geom., Volume 99, Number 1 (2015), 47-75.

First available in Project Euclid: 12 December 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Andrews, Ben; Langford, Mat; McCoy, James. Convexity estimates for surfaces moving by curvature functions. J. Differential Geom. 99 (2015), no. 1, 47--75. doi:10.4310/jdg/1418345537.

Export citation