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On a non-local area-preserving curvature flow in the plane

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Abstract

In this paper, we consider a kind of area-preserving flow for closed convex planar curves which will decrease the length of the evolving curve and make the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle as time \(t\rightarrow +\infty \).

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Acknowledgements

I’m grateful to the anonymous referee for his or her careful reading of the original manuscript of this short paper and giving me many helpful suggestions and invaluable comments.

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Correspondence to Zezhen Sun.

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Communicated by Herr Cortés.

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Sun, Z. On a non-local area-preserving curvature flow in the plane. Abh. Math. Semin. Univ. Hambg. 91, 345–352 (2021). https://doi.org/10.1007/s12188-021-00249-9

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  • DOI: https://doi.org/10.1007/s12188-021-00249-9

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