Abstract
We use two simple methods to derive four important explicit graphical solutions of the curve shortening flow in the plane. They are well-known as the circle, hairclip, paperclip, and grim reaper solutions of the curve shortening flow. By the methods, one can also see that the hairclip and the paperclip solutions both converge to the grim reaper solutions as t → −∞.
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Acknowledgements
The material in Section 3 (except Lemma 3.6) is due to Professors Yng-Ing Lee, Mao-Pei Tsui, and Dr. Kuo-Wei Lee of the National Taiwan University. The authors thank them for their kind help.
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Research of the first author was supported by MoST of Taiwan under grant number 105-2115-M-007-013 and research of the second author was supported by NSF of Jiangsu Province (BK20161412), and the Postdoctoral Science Foundation of China (2016T90399, 2014M561542).
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Tsai, DH., Wang, X. On Some Simple Methods to Derive the Hairclip and Paperclip Solutions of the Curve Shortening Flow. Acta Math Sci 39, 1674–1694 (2019). https://doi.org/10.1007/s10473-019-0616-5
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DOI: https://doi.org/10.1007/s10473-019-0616-5