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Inverse curvature flows in hyperbolic space

Claus Gerhardt Ruprecht-Karls-Universitat Institut fur Angewandte Mathematik

Differential Geometry mathscidoc:1609.10245

Journal of Differential Geometry, 89, (3), 487-527, 2011
We consider inverse curvature ows in Hn+1 with star-shaped initial hypersurfaces and prove that the ows exist for all time, and that the leaves converge to in nity, become strongly convex exponentially fast and also more and more totally umbilic. Afteran appropriate rescaling the leaves converge in C1 to a sphere.
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@inproceedings{claus2011inverse,
  title={INVERSE CURVATURE FLOWS IN HYPERBOLIC SPACE},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211422254043906},
  booktitle={Journal of Differential Geometry},
  volume={89},
  number={3},
  pages={487-527},
  year={2011},
}
Claus Gerhardt. INVERSE CURVATURE FLOWS IN HYPERBOLIC SPACE. 2011. Vol. 89. In Journal of Differential Geometry. pp.487-527. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211422254043906.
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