Mean curvature flow of pinched submanifolds to spheres

Ben Andrews Australian National University Charles Baker Ben.Andrews@maths.anu.edu.au

Differential Geometry mathscidoc:1609.10186

Journal of Differential Geometry, 85, (3), 357-395, 2010
We consider compact submanifolds of dimension n  2 in Rn+k, with nonzero mean curvature vector everywhere, and such that the full norm of the second fundamental form is bounded by a fixed multiple (depending on n) of the length of the mean curvature vector at every point. We prove that the mean curvature flow deforms such a submanifold to a point in finite time, and that the solution is asymptotic to a shrinking sphere in some (n + 1)- dimensional affine subspace of Rn+k.
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@inproceedings{ben2010mean,
  title={MEAN CURVATURE FLOW OF PINCHED SUBMANIFOLDS TO SPHERES},
  author={Ben Andrews, and Charles Baker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911220424837922843},
  booktitle={Journal of Differential Geometry},
  volume={85},
  number={3},
  pages={357-395},
  year={2010},
}
Ben Andrews, and Charles Baker. MEAN CURVATURE FLOW OF PINCHED SUBMANIFOLDS TO SPHERES. 2010. Vol. 85. In Journal of Differential Geometry. pp.357-395. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911220424837922843.
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