On the Saddle Point Property of Abresch-Langer curves under the Curve Shortening Flow

Thomas Kwok-keung Au

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On the Saddle Point Property of Abresch-Langer curves under the Curve Shortening Flow

Thomas Kwok-keung Au

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Abstract

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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BibTeX RIS

Thomas Kwok-keung Au. 2001-02-13. On the Saddle Point Property of Abresch-Langer curves under the Curve Shortening Flow. https://arxiv.org/abs/math/0102088

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