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A Grayson-type theorem for star-shaped curves

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Abstract

This paper focuses on a length-preserving flow for star-shaped curves with respect to the origin. Under the length-preserving flow, the evolving curve keeps star-shapedness and converges smoothly to a circle, which can be regarded as a Grayson-type theorem for star-shaped curves under this flow.

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Acknowledgements

The authors would like to express their gratitude to the referee for the diligent review and valuable comments. Special thanks are also extended to Laiyuan Gao for providing valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, People’s Republic of China

    Jianbo Fang & Fangwei Chen

  2. School of Science, Dalian Maritime University, Dalian, 116026, People’s Republic of China

    Yunlong Yang

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  1. Jianbo Fang
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  2. Yunlong Yang
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  3. Fangwei Chen
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Correspondence to Jianbo Fang.

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The work is supported by the National Natural Science Foundation of China (No. 11861004), research project of Guizhou University of Finance and Economics (2022XSXMB15), and the Fundamental Research Funds for the Central Universities (Nos. 3132023202, 3132022206).

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Fang, J., Yang, Y. & Chen, F. A Grayson-type theorem for star-shaped curves. Collect. Math. (2023). https://doi.org/10.1007/s13348-023-00425-5

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