Volume preserving flow by powers of k-th mean curvature

Ben Andrews Australian National University Yong Wei Australian National University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1908.10009

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.
Volume preserving flow, Mixed volume, curvature measure.
[ Download ] [ 2019-08-19 18:48:24 uploaded by WeiYong ] [ 719 downloads ] [ 0 comments ]
  • accepted by Journal of Differential Geometry
  title={Volume preserving flow by powers of k-th mean curvature},
  author={Ben Andrews, and Yong Wei},
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.
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