caa a22 4500 445836032 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0637-1 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0637-1 On the extension of the mean curvature flow [Elektronische Daten] [Nam Le, Natasa Sesum] Consider a family of smooth immersions $${F(\cdot,t): M^n\to \mathbb{R}^{n+1}}$$ of closed hypersurfaces in $${\mathbb{R}^{n+1}}$$ moving by the mean curvature flow $${\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)}$$, for $${t\in [0,T)}$$. Cooper (Mean curvature blow up in mean curvature flow, arxiv.org/abs/0902.4282) has recently proved that the mean curvature blows up at the singular time T. We show that if the second fundamental form stays bounded from below all the way to T, then the scaling invariant mean curvature integral bound is enough to extend the flow past time T, and this integral bound is optimal in some sense explained below. Springer-Verlag, 2009 Le Nam Department of Mathematics, Columbia University, New York, NY, USA aut Sesum Natasa Department of Mathematics, Columbia University, New York, NY, USA aut Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 583-604 0025-5874 267:3-4<583 2011 267 209 https://doi.org/10.1007/s00209-009-0637-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0637-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Le Nam Department of Mathematics, Columbia University, New York, NY, USA aut NATIONALLICENCE 700 1- Sesum Natasa Department of Mathematics, Columbia University, New York, NY, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 583-604 0025-5874 267:3-4<583 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer