A New Length Estimate for Curve Shortening Flow and Low Regularity Initial Data

@article{Lauer2011ANL,
title={A New Length Estimate for Curve Shortening Flow and Low Regularity Initial Data},
author={Joseph Lauer},
journal={Geometric and Functional Analysis},
year={2011},
volume={23},
pages={1934-1961}
}
• Joseph Lauer
• Published 24 February 2011
• Mathematics
• Geometric and Functional Analysis
In this paper we introduce a geometric quantity, the r-multiplicity, that controls the length of a smooth curve as it evolves by curve shortening flow (CSF). The length estimates we obtain are used to prove results about the level set flow in the plane. If K is locally-connected, connected and compact, then the level set flow of K either vanishes instantly, fattens instantly or instantly becomes a smooth closed curve. If the compact set in question is a Jordan curve J, then the proof proceeds…

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