Skip to main content
placeholder image

Curvature contraction of convex hypersurfaces by nonsmooth speeds

Journal Article


Download full-text (Open Access)

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.

Publication Date


  • 2017

Citation


  • 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, 2017 (727), 169-190.

Scopus Eid


  • 2-s2.0-84990232470

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1199&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/198

Number Of Pages


  • 21

Start Page


  • 169

End Page


  • 190

Volume


  • 2017

Issue


  • 727

Place Of Publication


  • Germany

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.

Publication Date


  • 2017

Citation


  • 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, 2017 (727), 169-190.

Scopus Eid


  • 2-s2.0-84990232470

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1199&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/198

Number Of Pages


  • 21

Start Page


  • 169

End Page


  • 190

Volume


  • 2017

Issue


  • 727

Place Of Publication


  • Germany