# 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} }

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…

## 11 Citations

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