Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature

Ben Andrews
2002 Communications in analysis and geometry  
We consider curvature-driven evolution equations for curves in the plane, and prove that the isoperimetric ratios of the evolving curves generically approach infinity if the speed of motion is proportional to curvature to a power less than 1/3.
doi:10.4310/cag.2002.v10.n2.a8 fatcat:6aegoarq6bg5jp4ule5yabk5he