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...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 → -∞.展开更多
基金supported by MoST of Taiwan under grant number 105-2115-M-007-013supported by NSF of Jiangsu Province(BK20161412)the Postdoctoral Science Foundation of China(2016T90399,2014M561542)
文摘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 → -∞.
