TY - JOUR
T1 - On some simple examples of non-parabolic curve flows in the plane
AU - Lin, Yu Chu
AU - Tsai, Dong Ho
AU - Wang, Xiao Liu
N1 - Publisher Copyright:
© 2015, Springer Basel.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We discuss several examples of non-parabolic curve flows in the plane. In these flows, the speed functions do not involve the curvature at all. Although elementary in nature, there are some interesting properties. In particular, certain non-parabolic flows can be employed to evolve a convex closed curve to become circular or to evolve a non-convex curve to become convex eventually, like what we have seen in the classical curve shortening flow (parabolic flow) by Gage and Hamilton (J Differ Geom 23:69–96, 1986), Grayson (J Differ Geom 26:285–314, 1987).
AB - We discuss several examples of non-parabolic curve flows in the plane. In these flows, the speed functions do not involve the curvature at all. Although elementary in nature, there are some interesting properties. In particular, certain non-parabolic flows can be employed to evolve a convex closed curve to become circular or to evolve a non-convex curve to become convex eventually, like what we have seen in the classical curve shortening flow (parabolic flow) by Gage and Hamilton (J Differ Geom 23:69–96, 1986), Grayson (J Differ Geom 26:285–314, 1987).
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U2 - 10.1007/s00028-015-0282-6
DO - 10.1007/s00028-015-0282-6
M3 - Article
AN - SCOPUS:84948063912
VL - 15
SP - 817
EP - 845
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
IS - 4
ER -