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

Research Report MRR00-006

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

Ben Andrews

Abstract: We prove that the isoperimetric ratios of evolving curves generically approach infinity if the speed of motion is proportional to curvature to a power less than 1/3.

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