TY - JOUR
T1 - Curvature contraction of convex hypersurfaces by nonsmooth speeds
AU - Andrews, Ben
AU - Holder, Andrew
AU - McCoy, James
AU - Wheeler, Glen
AU - Wheeler, Valentina Mira
AU - Williams, Graham
PY - 2017/6
Y1 - 2017/6
N2 - 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 C2 sense, with the convergence being exponential.
AB - 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 C2 sense, with the convergence being exponential.
UR - http://www.scopus.com/inward/record.url?scp=85029220807&partnerID=8YFLogxK
U2 - 10.1515/crelle-2014-0087
DO - 10.1515/crelle-2014-0087
M3 - Article
AN - SCOPUS:85029220807
SN - 0075-4102
VL - 2017
SP - 169
EP - 190
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 727
ER -