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→-∞.
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
.
DOI: 10.1007/s10473-019-0616-5
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