A Note on Self-Similar Solutions of the Curve Shortening

Márcio Adames

Resumo


This article gives an alternative approach to the self-shrinking and self-expanding solutions of the curve shortening flow, which are related to singularity formation of the mean curvature flow. Further we describe the self-similar solutions in terms of a simple ODE and give an alternative proof that they lie in planes.


Palavras-chave


Curve Shortening Flow, Abresch & Langer Curves, Planar Solutions.

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DOI: https://doi.org/10.5540/03.2017.005.01.0022

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