Quermassintegral preserving curvature flow in hyperbolic space

Ben Andrews Australian National University Yong Wei Australian National University

Analysis of PDEs Differential Geometry mathscidoc:1810.03002

Distinguished Paper Award in 2018

Geometric and Functional Analysis, 28, 1183–1208, 2018.10
We consider the quermassintegral preserving flow of closed \emph{h-convex} hypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one function $f$ of the principal curvatures which is inverse concave and has dual $f_*$ approaching zero on the boundary of the positive cone. We prove that if the initial hypersurface is \emph{h-convex}, then the solution of the flow becomes strictly \emph{h-convex} for $t>0$, the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology.
Quermassintegral preserving flow, hyperbolic space, Alexandrov reflection.
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@inproceedings{ben2018quermassintegral,
  title={Quermassintegral preserving curvature flow in hyperbolic space},
  author={Ben Andrews, and Yong Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181030170519773694169},
  booktitle={Geometric and Functional Analysis},
  volume={28},
  pages={1183–1208},
  year={2018},
}
Ben Andrews, and Yong Wei. Quermassintegral preserving curvature flow in hyperbolic space. 2018. Vol. 28. In Geometric and Functional Analysis. pp.1183–1208. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181030170519773694169.
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