On the saddle point property of Abresch–Langer curves under the curve shortening flow

@article{Au2001OnTS,
  title={On the saddle point property of Abresch–Langer curves under the curve shortening flow},
  author={Thomas Kwok-keung Au},
  journal={Communications in Analysis and Geometry},
  year={2001},
  volume={18},
  pages={1-21}
}
  • T. Au
  • Published 12 February 2001
  • Mathematics
  • Communications in Analysis and Geometry
In the study of the curve shortening flow on general closed curves, Abresch and Langer posed a conjecture that the homothetic curves can be regarded as saddle points between multi-folded circles and some singular curves. In other words, these homothetic curves are the watershed between curves with a nonsingular future and those with singular future along the flow. In this article, we provide an affirmitive proof to this conjecture. 

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