Expansion of embedded curves with turning angle greater than \(-\pi\)
Recently, the first and third author [J. Differ. Geom., to appear] showed that closed convex curves in the plane expanding by a positive function of their curvature expand to infinity and become asymptotically round. The third author [Comm. Anal. Geom. 4, No. 3, 459-480 (1996)] extended this result to starshaped initial curves. Here the authors carry this a step further by showing that for a certain general class of closed embedded initial curves, the solutions become starshaped and then convex after a finite time, and then asymptotically round.
scientific article; zbMATH DE number 922456
scientific article