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Inverse Curvature Flows in Hyperbolic Space

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Differential Geometry mathscidoc:1609.10342

JDG, 89, (3), 487-527, 2011
We consider inverse curvature flows in $\Hh$ with star-shaped initial hypersurfaces and prove that the flows exist for all time, and that the leaves converge to infinity, become strongly convex exponentially fast and also more and more totally umbilic. After an appropriate rescaling the leaves converge in $C^\infty$ to a sphere.
curvature flows, inverse curvature flows, hyperbolic space
[ Download ] [ 2016-09-23 05:55:10 uploaded by gerhardt ] [ 1499 downloads ] [ 0 comments ] 
@inproceedings{claus2011inverse,
  title={Inverse Curvature Flows in Hyperbolic Space},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160923055510811920045},
  booktitle={JDG},
  volume={89},
  number={3},
  pages={487-527},
  year={2011},
}
Claus Gerhardt. Inverse Curvature Flows in Hyperbolic Space. 2011. Vol. 89. In JDG. pp.487-527. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160923055510811920045.
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