Ben AndrewsAustralian National UniversityYong WeiAustralian National University
Differential GeometryGeometric Analysis and Geometric Topologymathscidoc:1908.10009
2017.8
We consider the flow of closed convex hypersurfaces in Euclidean space R^{n+1} with speed given by a power of the k-th mean curvature E_k plus a global term chosen to impose a constraint involving the enclosed volume V_{n+1} and the mixed volume V_{n+1−k} of the evolving hypersurface. We prove that if the initial hypersurface is strictly convex, then the solution of the flow exists for all time and converges to a round sphere smoothly. No curvature pinching assumption is required on the initial hypersurface.
@inproceedings{ben2017volume,
title={Volume preserving flow by powers of k-th mean curvature},
author={Ben Andrews, and Yong Wei},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819184824861716416},
year={2017},
}
Ben Andrews, and Yong Wei. Volume preserving flow by powers of k-th mean curvature. 2017. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819184824861716416.