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Existence of Self-similar Solutions to the Anisotropic Affine Curve-shortening Flow

Jian Lu

Geometric Analysis and Geometric Topology mathscidoc:1910.43010

International Mathematics Research Notices, 2018.11
In this paper the existence of positive 2\pi -periodic solutions to the ordinary differential equation \begin{equation*} u^{\prime\prime}+u=\frac{f}{u^3} \ \textrm{ in } \mathbb{R} \end{equation*}is studied, where 2\pi is a positive 2\pi -periodic smooth function. By virtue of a new generalized Blaschke鈥揝antal贸 inequality, we obtain a new existence result of solutions.
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@inproceedings{jian2018existence,
  title={Existence of Self-similar Solutions to the Anisotropic Affine Curve-shortening Flow},
  author={Jian Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007231450912817539},
  booktitle={International Mathematics Research Notices},
  year={2018},
}
Jian Lu. Existence of Self-similar Solutions to the Anisotropic Affine Curve-shortening Flow. 2018. In International Mathematics Research Notices. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007231450912817539.
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