Corpus ID: 235458337

Optimal thresholds for preserving embeddedness of elastic flows

  title={Optimal thresholds for preserving embeddedness of elastic flows},
  author={Tatsuya Miura and Marius Muller and Fabian Rupp},
We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. The obtained thresholds take different values between codimension one and higher. The main novelty lies in the case of codimension one, where we obtain the variational characterization that the thresholding shape is a minimizer of the bending energy (normalized by length) among all nonembedded planar closed curves of… Expand

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