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We present a numerical scheme for axisymmetric solutions to curvature driven moving bound ary problems governed by a local law of motion, e.g. the mean curvature ow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore ow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in nite time.

A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow