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Asymptotic behavior of flows by powers of the Gaussian curvature

Simon Brendle Columbia University Kyeongsu Choi Columbia University Panagiota Daskalopoulos Columbia University

Differential Geometry mathscidoc:1911.43012

Acta Mathematica, 219, (1), 1 – 16, 2017
We consider a 1-parameter family of strictly convex hypersurfaces in Rn+1 moving with speed −Kαν, where ν denotes the outward-pointing unit normal vector and α⩾1/(n+2). For α>1/(n+2), we show that the flow converges to a round sphere after rescaling. In the affine invariant case α=1/(n+2), our arguments give an alternative proof of the fact that the flow converges to an ellipsoid after rescaling.
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@inproceedings{simon2017asymptotic,
  title={Asymptotic behavior of flows by powers of the Gaussian curvature},
  author={Simon Brendle, Kyeongsu Choi, and Panagiota Daskalopoulos},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126154723386372523},
  booktitle={Acta Mathematica},
  volume={219},
  number={1},
  pages={1 – 16},
  year={2017},
}
Simon Brendle, Kyeongsu Choi, and Panagiota Daskalopoulos. Asymptotic behavior of flows by powers of the Gaussian curvature. 2017. Vol. 219. In Acta Mathematica. pp.1 – 16. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126154723386372523.
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