English

Legendrian curve shortening flow in $\mathbb{R}^{3}$

Differential Geometry 2015-08-06 v1

Abstract

Motivated by Legendrian curve shortening flows in R3\mathbb{R}^{3}, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time.

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Cite

@article{arxiv.1508.01186,
  title  = {Legendrian curve shortening flow in $\mathbb{R}^{3}$},
  author = {Gregory Drugan and Weiyong He and Micah W. Warren},
  journal= {arXiv preprint arXiv:1508.01186},
  year   = {2015}
}
R2 v1 2026-06-22T10:27:20.038Z