ON SOME SIMPLE METHODS TO DERIVE THE HAIRCLIP AND PAPERCLIP SOLUTIONS OF THE CURVE SHORTENING FLOW

doi:10.1007/s10473-019-0616-5

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (6): 1674-1694.doi: 10.1007/s10473-019-0616-5

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ON SOME SIMPLE METHODS TO DERIVE THE HAIRCLIP AND PAPERCLIP SOLUTIONS OF THE CURVE SHORTENING FLOW

Dong-Ho TSAI¹, Xiaoliu WANG²

1. Department of Mathematics, National Tsing Hua University, Hsinchu 30013, China;
2. Department of Mathematics, Southeast University, Nanjing 210096, China

Received:2018-03-13 Revised:2019-05-09 Online:2019-12-25 Published:2019-12-30
Contact: Dong-Ho TSAI,E-mail:dhtsai@math.nthu.edu.tw E-mail:dhtsai@math.nthu.edu.tw
Supported by:
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).

Abstract

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→-∞.

Key words: curve shortening flow, grim reaper solution, hairclip solution, paperclip solution

CLC Number:

53C44

Dong-Ho TSAI, Xiaoliu WANG. ON SOME SIMPLE METHODS TO DERIVE THE HAIRCLIP AND PAPERCLIP SOLUTIONS OF THE CURVE SHORTENING FLOW[J].Acta mathematica scientia,Series B, 2019, 39(6): 1674-1694.

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References

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ON SOME SIMPLE METHODS TO DERIVE THE HAIRCLIP AND PAPERCLIP SOLUTIONS OF THE CURVE SHORTENING FLOW

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