The Zoo of Solitons for Curve Shortening in $\R^n$

  title={The Zoo of Solitons for Curve Shortening in \$\R^n\$},
  author={Dylan J.Altschuler and Steven J.Altschuler and Sigurd B.Angenent and Lani F.Wu},
We provide a detailed description of solutions of Curve Shortening in Rn that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic properties of their ends. We find generalized helices, and a connection with curve shortening on the unit sphere Sn−1. Expanding rotating solitons turn out to be asymptotic to generalized logarithmic spirals. In terms of asymptotic properties of their ends the… 

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