Abstract
In this paper we prove that the \(H^{k}\) (\(k\) is odd and larger than \(2\)) mean curvature flow of a closed convex hypersurface can be extended over the maximal time provided that the total \(L^{p}\) integral of the mean curvature is finite for some \(p\).
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Huisken, G.: Flow by mean curvature of convex surfaces into spheres. J. Differ. Geom. 20(1), 237–266 (1984). MR0772132 (86j: 53097)
Le, N.Q., Sesum, N.: On the extension of the mean curvature flow. Math. Z. 267(3–4), 583–604 (2011). MR2776050 (2012h: 53153)
Li, Y.: On an extension of the \(H^{k}\) mean curvature flow. Sci. China Math. 55(1), 99–118 (2012). MR2873806
Smoczyk, K.: Harnack inequalities for curvature flows depending on mean curvature. New York J. Math. 3, 103–118 (1997). MR1480081 (98i: 53056)
Xu, H.-W., Ye, F., Zhao, E.-T.: Extend mean curvature flow with finite integral curvature. Asian J. Math. 15(4), 549–556 (2011). MR2853649 (2012h: 53158)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Y. On an extension of the \(H^{k}\) mean curvature flow of closed convex hypersurfaces. Geom Dedicata 172, 147–154 (2014). https://doi.org/10.1007/s10711-013-9912-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-013-9912-8