# MathSciDoc: An Archive for Mathematician ∫

#### 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.
@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.