Corpus ID: 235456434

The Affine Shape of a Figure-Eight under the Curve Shortening Flow

@inproceedings{Coiculescu2021TheAS,
  title={The Affine Shape of a Figure-Eight under the Curve Shortening Flow},
  author={Matei P. Coiculescu and R. Schwartz},
  year={2021}
}
We consider the curve shortening flow applied to a natural class of figureeight curves, those with dihedral symmetry and some monotonicity assumptions on the curvature and its derivatives. We prove that when (non-conformal) linear transformations are applied to the solution so as to keep the bounding box the unit square, the renormalized limit converges to a quadrilateral ⋊⋉ called a bowtie. Along the way we prove that suitably chosen arcs of our evolving curves, when suitably rescaled… Expand

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