New Pinching Estimates for Inverse Curvature Flows in Space Forms

Yong Wei Australian National University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1908.10010

The Journal of Geometric Analysis, 29, (2), 1555-1570, 2019.4
We consider the inverse curvature flow of strictly convex hypersurfaces in the space form N of constant sectional curvature K_N with speed given by F^{−α}, where α∈(0,1] for K_N=0,−1 and α=1 for K_N=1, F is a smooth, symmetric homogeneous of degree one function which is inverse concave and has dual F_∗ approaching zero on the boundary of the positive cone Γ_+. We show that the ratio of the largest principal curvature to the smallest principal curvature of the flow hypersurface is controlled by its initial value. This can be used to prove the smooth convergence of the flows.
Pinching estimate, Inverse curvature flow, Space form, Inverse concave
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@inproceedings{yong2019new,
  title={New Pinching Estimates for Inverse Curvature Flows in Space Forms},
  author={Yong Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820062649700322417},
  booktitle={The Journal of Geometric Analysis},
  volume={29},
  number={2},
  pages={1555-1570},
  year={2019},
}
Yong Wei. New Pinching Estimates for Inverse Curvature Flows in Space Forms. 2019. Vol. 29. In The Journal of Geometric Analysis. pp.1555-1570. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820062649700322417.
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