The normalized curve shortening flow and homothetic solutions

  title={The normalized curve shortening flow and homothetic solutions},
  author={Uwe Abresch and James Langer},
  journal={Journal of Differential Geometry},
The curve shortening problem, by now widely known, is to understand the evolution of regular closed curves γ: R/Z -> M moving according to the curvature normal vector: dy/dt = kN = -"the ZΛgradient of arc length". One motivation for this problem has been the view expressed in this connection by C. Croke, H. Gluck, W. Ziller, and others: it would be desirable to improve on some complicated and ad hoc constructions that have been used in the theory of closed geodesies to iteratively shorten… 

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