Convexity estimates for surfaces moving by curvature functions

Authors

Ben Andrews, Australian National UniversityFollow
Mat Langford, Australian National UniversityFollow
James A. McCoy, University of WollongongFollow

RIS ID

88667

Publication Details

Andrews, B., Langford, M. & McCoy, J. (2015). Convexity estimates for surfaces moving by curvature functions. Journal of Differential Geometry, 99 (1), 47-75.

Abstract

We consider the evolution of compact surfaces by fully nonlinear, parabolic curvature ows 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 [26] of Huisken and Sinestrari for the mean curvature ow to the largest possible class of degree one homogeneous surface flows.

Grant Number

ARC/DP0556211, ARC/DP120100097

Additional Grant Number

http://purl.org/au-research/grants/arc/DP0556211

http://purl.org/au-research/grants/arc/DP120100097