Non existence of Type II singularities for embedded and unknotted space curves

Karen Corrales

Non existence of Type II singularities for embedded and unknotted space curves

Differential Geometry 2016-05-11 v1

Authors: Karen Corrales

Abstract

In this paper we prove that a certain class of embedded unknotted curves in $\mathbb{R}^3$ evolving under curve shortening flow do not form singularities Type II before collapsing to a point. Our proof uses tools of the minimal surface theory to study a suitable isoperimetric ratio.

Keywords

curve shortening flow embedded unknotted curves Type II singularities minimal surface theory isoperimetric ratio

Cite

@article{arxiv.1605.03100,
  title  = {Non existence of Type II singularities for embedded and unknotted space curves},
  author = {Karen Corrales},
  journal= {arXiv preprint arXiv:1605.03100},
  year   = {2016}
}

Comments

18 pages, 3 figures

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