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A note on self-similar solutions of the curve shortening flow (1505.07435v2)
Published 27 May 2015 in math.DG
Abstract: 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. The motivation for the self-similar solutions arises from natural area preserving rescaling. Further we describe the self-similar solutions in terms of a simple ODE and give an alternative proof that they lie in planes.
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