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 \(p\).
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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)
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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
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DOI: https://doi.org/10.1007/s10711-013-9912-8