On the saddle point property of abresch-langer curves under the curve shortening flow
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AbstractIn the study of the curve shortening flow on general closed curves in the plane, Abresch and Langer posed a conjecture that the homothetic curves can be regarded as saddle points between multi-folded circles and certain 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 affirmative proof to this conjecture.
All Author(s) ListAu T.K.-K.
Journal nameCommunications in Analysis and Geometry
Volume Number18
Issue Number1
PublisherInternational Press
Place of PublicationUnited States
Pages1 - 21
LanguagesEnglish-United Kingdom

Last updated on 2020-28-10 at 01:10