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Higher regularity of the inverse mean curvature flow

Gerhard Huisken Albert-Einstein-Institut, Am M¨uhlenberg Tom Ilmanen ETH Zentrum, R¨amistrasse 101

Differential Geometry mathscidoc:1609.10086

Journal of Differential Geometry, 80, (3), 433-451, 2008
We prove higher regularity properties of inverse mean curvature flow in Euclidean space: A sharp lower bound for the mean curvature is derived for star-shaped surfaces, independently of the initial mean curvature. It is also shown that solutions to the inverse mean curvature flow are smooth if the mean curvature is bounded from below. As a consequence we show that weak solutions of the inverse mean curvature flow are smooth for large times,beginning from the first time where a surface in the evolution is star-shaped.
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@inproceedings{gerhard2008higher,
  title={HIGHER REGULARITY OF THE INVERSE MEAN CURVATURE FLOW},
  author={Gerhard Huisken, and Tom Ilmanen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909140359875629743},
  booktitle={Journal of Differential Geometry},
  volume={80},
  number={3},
  pages={433-451},
  year={2008},
}
Gerhard Huisken, and Tom Ilmanen. HIGHER REGULARITY OF THE INVERSE MEAN CURVATURE FLOW. 2008. Vol. 80. In Journal of Differential Geometry. pp.433-451. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909140359875629743.
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