# 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} }

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.

## 14 Citations

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