On some simple examples of non-parabolic curve flows in the plane (Q904341)

The authors studies several examples of non-parabolic curve flows in the plane with speed function that is independent of the curvature. These include the unit speed outward normal flow (USONF), normal component flow or rescaling flow (REF), tangential component flow or rotational flow (ROF) and a combination of UNSOF and REF. They prove that some of these non-parabolic flows will evolve a convex closed curve to circle and some will evolve a non-convex curve to become convex eventually similar to the results for the classical curve shortening flow by \textit{M. Gage} and \textit{R. S. Hamilton} [J. Differ. Geom. 23, 69--96 (1986; Zbl 0621.53001)] and by \textit{M. A. Grayson} [J. Differ. Geom. 26, 285--314 (1987; Zbl 0667.53001)].