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Hyperbolic geometric flow (I): short-time existence and nonlinear stability

Wen-Rong Dai De-Xing Kong Kefeng Liu

Differential Geometry mathscidoc:1912.43065

Pure and Applied Mathematics Quarterly, 6, (2), 331-359, 2010.4
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave equations satisfied by the curvatures are derived. The relations of the hyperbolic geometric flow with the Einstein equations and the Ricci flow are discussed.
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@inproceedings{wen-rong2010hyperbolic,
  title={Hyperbolic geometric flow (I): short-time existence and nonlinear stability},
  author={Wen-Rong Dai, De-Xing Kong, and Kefeng Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111337520428625},
  booktitle={Pure and Applied Mathematics Quarterly},
  volume={6},
  number={2},
  pages={331-359},
  year={2010},
}
Wen-Rong Dai, De-Xing Kong, and Kefeng Liu. Hyperbolic geometric flow (I): short-time existence and nonlinear stability. 2010. Vol. 6. In Pure and Applied Mathematics Quarterly. pp.331-359. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111337520428625.
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