Curvature contraction of convex hypersurfaces by nonsmooth speeds

Authors

Ben H. Andrews, Australian National UniversityFollow
Andrew Brett Holder, University of WollongongFollow
James A. McCoy, University of WollongongFollow
Glen Wheeler, University of WollongongFollow
V.-M Wheeler, University of WollongongFollow
Graham H. Williams, University of WollongongFollow

RIS ID

94613

Publication Details

Andrews, B., Holder, A., McCoy, J., Wheeler, G., Wheeler, V. & Williams, G. (2017). Curvature contraction of convex hypersurfaces by nonsmooth speeds. Journal für die reine und angewandte Mathematik, 727 169-190.

Abstract

We consider contraction of convex hypersurfaces by convex speeds, homogeneous of degree one in the principal curvatures, that are not necessarily smooth. We show how to approximate such a speed by a sequence of smooth speeds for which behaviour is well known. By obtaining speed and curvature pinching estimates for the flows by the approximating speeds, independent of the smoothing parameter, we may pass to the limit to deduce that the flow by the nonsmooth speed converges to a point in finite time that, under a suitable rescaling, is round in the C^2 sense, with the convergence being exponential.

Grant Number

ARC/DP120100097